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Mathematics Chapter 4 Principle Of Mathematical Induction

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NCERT Solution For Class 11 Mathematics

Principle Of Mathematical Induction Here is the CBSE Mathematics Chapter 4 for Class 11 students. Summary and detailed explanation of the lesson, including the definitions of difficult words. All of the exercises and questions and answers from the lesson's back end have been completed. NCERT Solutions for Class 11 Mathematics Principle Of Mathematical Induction Chapter 4 NCERT Solutions for Class 11 Mathematics Principle Of Mathematical Induction Chapter 4 The following is a summary in Hindi and English for the academic year 2021-2022. You can save these solutions to your computer or use the Class 11 Mathematics.

Question 1

Mathematics Chapter 4 Principle Of Mathematical Induction

NCERT Solution For Class 11 Mathematics

Convert to radians

Convert to degrees.

Find 1 radian angle in degrees, minutes, seconds.

Find the radian measures corresponding to the following degree measure:

Find the radian measures corresponding to the following degree measure:

Find the radian measures corresponding to the following degree measure:

Find the radian measures corresponding to the following degree measure:

“Express in radians the angle 50° 37’ 30” .

Find the degree measure corresponding to the following radian measure:

Find the degree measure corresponding to the following radian measure:

Find the degree measure corresponding to the following radian measure:

Find the degree measure corresponding to the following radian measure:

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

A wheel rotates through an angle of radians in one second. How many revolutions will it make in 5 minutes?

The difference between two acute angles of a right angled triangle is Express the angles in: (a) degrees (b) radians.

If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use ).

A circular wire of radius 7.5 cm is cut and bent so as to lie along the circumference of a circular hoop whose radius is 120 cm. Find, in degrees, the angle which is subtended at the centre of this hoop.

A railway train is travelling on a circular track of 1500 m radius at the speed of 66 km/h. Through what angle (in degrees) does it turn in 10 seconds ?

An athlete runs 4 times around a circular running path to describe 1760 metres. What is the angle in (i) radians, (ii) degrees subtended at the centre of the circle, when he had run a distance of 308 metres?

The angles of a triangle are in A.P. and the number of degrees in the least angle is to the number of radians in the greatest angle is 60 : . Find the angles in degrees.

Assuming the average distance of the earth from the sun to be 149,700,000 km, and the angle subtended by the sun at the eye of a person on the earth to be 32’, find the sun’s diameter.

Find the angle between the minute hand of a clock and the hour hand when the time is 7:20 A.M.

Find the values of other five trigonometric functions of the following: lies in third quadrant

Find the values of other five trigonometric functions of the following: lies in second quadrant

Find the values of other five trigonometric functions of the following: lies in third quadrant

Find the values of the trigonometric functions in the following:

Find the values of the trigonometric functions in the following:

Find the value of the trigonometric function in the following:

Find the value of the trigonometric function in the following:

Find the value of the trigonometric function in the following:

and x lies in third quadrant. Find the value of

Show that no value of θ can satisfy the equation:

Show that sec2 θ + cos2 θ can never be less than 2.

If x, y are real, show that is valid only when

Find the values of the following:

Find the value of the following:

Find the value of the following:

Find the value of the following:

Find the value of the following:

Prove that:

Prove that :

Prove that:

Prove that:

Show that:

Show that:

Show that:

Solve for x, when Also, find the value of x, when

In ∆ABC, prove that:

In ∆ABC, prove that:

In any quadrilateral ABCD, show that sin (A + B) + sin (C + D) = 0.

If A, B, C, D are the vertices of a cyclic quadrilateral, show that sin A + sin B - sin C - sin D = 0.

Show that :

Find the period of the following trigonometric functions:

Find the period of the following trigonometric functions:

Show that:

Find the value of:

Find the value of:

Find the value of:

Prove that:

Prove the following:

Prove the following:

If and where and find the value of State the quadrant in which terminates.

Prove that:

Prove that:

Prove that:

Prove the following:

Prove the following:

Show that:

Show that:

Show that:

Prove the following:

If A + B = , show that

Prove that

If show that

Show that;

If and where prove that

Prove the following;

Convert $negative 60 degree$ to radians

Convert $straight pi over 12$ to degrees.

Find the radian measures corresponding to the following degree measure:

$space 25 degree$

Find the radian measures corresponding to the following degree measure:

$negative 47 degree 30 apostrophe$

Find the radian measures corresponding to the following degree measure:

$240 to the power of ring operator$

Find the radian measures corresponding to the following degree measure:

$520 to the power of ring operator$

Find the degree measure corresponding to the following radian measure:

$fraction numerator 5 straight pi over denominator 3 end fraction$

Find the degree measure corresponding to the following radian measure:

$11 over 16$

Find the degree measure corresponding to the following radian measure:

$space space space space space fraction numerator 7 straight pi over denominator 6 end fraction$

A wheel rotates through an angle of $straight pi over 30$ radians in one second. How many revolutions will it make in 5 minutes?

The difference between two acute angles of a right angled triangle is $fraction numerator 2 straight pi over denominator 5 end fraction radians.$ Express the angles in: (a) degrees (b) radians.

Find the degree measure of the angle subtended at the centre of a circle of radius 100

cm by an arc of length 22 cm (Use $straight pi space equals space 22 over 7$ ).

An athlete runs 4 times around a circular running path to describe 1760 metres.

What is the angle in (i) radians, (ii) degrees subtended at the centre of the circle, when

he had run a distance of 308 metres? $open parentheses Take space straight pi space equals space 22 over 7 close parentheses$

The angles of a triangle are in A.P. and the number of degrees in the least angle is to the number of radians in the greatest angle is 60 : $straight pi$ . Find the angles in degrees.

Find the values of other five trigonometric functions of the following:

$cosx space equals space minus 1 half comma space straight x$ lies in third quadrant

Find the values of other five trigonometric functions of the following:

$sinx space equals space 3 over 5 comma space straight x$ lies in second quadrant

Find the values of other five trigonometric functions of the following:

$cotx space equals space 3 over 4 comma space space straight x$ lies in third quadrant

Find the values of the trigonometric functions in the following:

$sin space 765 degree$

Find the values of the trigonometric functions in the following:

$cosec left parenthesis negative 1410 degree right parenthesis$

Find the value of the trigonometric function in the following:

$tan open parentheses fraction numerator 19 straight pi over denominator 3 end fraction close parentheses$

Find the value of the trigonometric function in the following:

$cot open parentheses negative fraction numerator 15 straight pi over denominator 4 end fraction close parentheses$

$space space sinx space equals space minus 5 over 13$ and x lies in third quadrant. Find the value of $space space secx plus tanx.$

Show that no value of θ can satisfy the equation:

$6 sec squared straight theta space minus space 5 secθ space plus space 1 space equals 0$

Show that sec² θ + cos² θ can never be less than 2.

Find the values of the following:

$tan space 315 degree$

Find the value of the following:

$space sin open parentheses fraction numerator 5 straight pi over denominator 3 end fraction close parentheses$

Find the value of the following:

$space space cos left parenthesis negative 1125 degree right parenthesis$

Find the value of the following:

$space space space tan open parentheses negative 13 over 4 straight pi close parentheses$

Show that: $cos 24 degree plus cos 55 degree plus cos 125 degree plus cos 204 degree plus cos 300 degree space equals space 1 half$

In ∆ABC, prove that:

$space space space cos space left parenthesis straight A plus straight B right parenthesis plus cos space straight C space equals space 0$

Find the period of the following trigonometric functions:

$sin open parentheses fraction numerator 3 straight x over denominator 2 end fraction close parentheses$

Find the period of the following trigonometric functions:

$tan open parentheses fraction numerator 5 straight x over denominator 3 end fraction close parentheses$

Find the value of:

$sin open parentheses straight pi over 12 close parentheses$

Find the value of:

$space space space cos open parentheses fraction numerator 5 straight pi over denominator 12 end fraction close parentheses$

Prove that:

$sin squared straight A minus sin squared straight B space equals space sin left parenthesis straight A plus straight B right parenthesis. space sin left parenthesis straight A minus straight B right parenthesis$

Prove that:

$cos squared straight A minus sin squared straight B space equals space cos left parenthesis straight A plus straight B right parenthesis. space cos left parenthesis straight A minus straight B right parenthesis$

Prove the following:

$space space space space cos squared 2 straight x minus cos squared 6 straight x space equals space sin space 4 straight x space sin 8 straight x$

Show that:

$fraction numerator cos 18 degree plus sin 18 degree over denominator cos 18 degree minus sin 18 degree end fraction space equals space cot space 27 degree.$

Show that: $tan 5 straight x space minus space tan 3 straight x space minus space tan 2 straight x space equals space tan 5 straight x space tan 3 straight x space tan 2 straight x$

Prove the following:

$tan space 70 degree space equals space tan space 20 degree plus 2 space tan 50 degree$

If A + B = $45 degree$ ,

show that $left parenthesis 1 plus tanA right parenthesis space left parenthesis 1 plus tanB right parenthesis space equals space 2$

Find the maximum and minimum values of:

$straight a space cosx plus straight b space sinx$

Prove the following:

$cos 4 straight x space equals space 1 minus 8 sin squared straight x space cos squared straight x$

Prove the following:

$tan 4 straight x space equals space fraction numerator 4 tanx space left parenthesis 1 minus tan squared straight x right parenthesis over denominator 1 minus 6 tan squared straight x plus tan to the power of 4 straight x end fraction$

Prove that:

$fraction numerator sin 2 straight x over denominator 1 plus cos 2 straight x end fraction space equals space tanx$

Prove that:

$fraction numerator 1 plus sin 2 straight x minus cos 2 straight x over denominator 1 plus sin 2 straight x plus cos 2 straight x end fraction space equals space tanx$

If $tan open parentheses straight x over 2 close parentheses space equals space 3 over 4 comma$ find the value of:

$sin space straight x$

If $tan open parentheses straight x over 2 close parentheses space equals space 3 over 4 comma$ find the value of:

$space space cos space straight x$

If $tan open parentheses straight x over 2 close parentheses space equals space 3 over 4 comma$ find the value of:

tan x.

Show that: $space space space square root of 2 plus square root of 2 plus 2 space cos space 4 straight theta end root end root space equals space 2 cosθ$

$If space space tanx space equals space straight b over straight a comma$ find the value of $straight a space cos space 2 straight x space plus space straight b space sin space 2 straight x.$

Show that:

$8 cos cubed open parentheses straight pi over 9 close parentheses minus 6 cos open parentheses straight pi over 9 close parentheses space equals space 1$

Show that:

$cos 4 straight A space equals space 1 minus 8 cos squared straight A space plus space 8 cos to the power of 4 straight A$

Show that:

$cos space 6 straight A space equals space 32 space cos to the power of 6 straight A space minus space 48 space cos to the power of 4 straight A space plus space 18 space cos squared straight A space minus 1$

Show that:

$cos 20 degree space cos 40 degree space cos 60 degree space cos 80 degree space equals space 1 over 16$

Find the value of:

$space space tan open parentheses straight pi over 8 close parentheses$

Find the value of:

$space space tan open parentheses fraction numerator 11 straight pi over denominator 8 end fraction close parentheses$

Find the value of:

$cos straight pi over 8$

Prove that:

$tan space straight A space plus space tan space left parenthesis 60 degree plus straight A right parenthesis minus tan space left parenthesis 60 degree minus straight A right parenthesis space equals space 3 space tan space 3 straight A.$

Show that:

$cos straight pi over 7. space cos fraction numerator 2 straight pi over denominator 7 end fraction. space cos fraction numerator 4 straight pi over denominator 7 end fraction space equals space minus 1 over 8$

If $cosx space equals space 1 half open parentheses straight a plus 1 over straight a close parentheses comma$ show that: $cos 2 straight x space equals space 1 half open parentheses straight a squared plus 1 over straight a squared close parentheses$

If cos x = $1 half open parentheses straight a plus 1 over straight a close parentheses comma$ show that:

$cos 3 straight x space equals space 1 half open parentheses straight a cubed plus 1 over straight a cubed close parentheses$

Prove the following:

$fraction numerator sin 5 straight x plus sin 3 straight x over denominator cos 5 straight x plus cos 3 straight x end fraction space equals space tan 4 straight x$

Prove the following:

$space space space fraction numerator sin space straight x minus sin space 3 straight x over denominator sin squared space straight x minus cos squared space straight x end fraction space equals space 2 space sin space straight x$

Prove the following:

$fraction numerator cos space 4 straight x plus cos space 3 straight x plus cos space 2 straight x over denominator sin space 4 straight x plus sin space 3 straight x plus sin space 2 straight x end fraction equals space cot space 3 straight x$

Show that: $sin space 51 degree space plus space cos space 81 degree space equals space cos space 21 degree$

Show that:

$fraction numerator sin 11 straight x space sinx space plus space sin 7 straight x space sin 3 straight x over denominator cos 11 straight x space sinx space plus space cos space 7 straight x space sin 3 straight x end fraction$ = tan 8x

Prove the following:

$sin space 2 straight x space plus space 2 space sin space 4 straight x space plus space sin space 6 straight x space equals space 4 cos squared space straight x space sin space 4 straight x$

Prove that:

$2 space cos straight pi over 13 space cos fraction numerator 9 straight pi over denominator 13 end fraction plus cos fraction numerator 3 straight pi over denominator 13 end fraction plus cos fraction numerator 5 straight pi over denominator 13 end fraction space equals space 0$

If cos (A + B) sin (C - D) = cos (A - B) sin (C + D)

Show that: tan A tan B tan C + tan D = 0

Show that: $left parenthesis sin space 3 straight x space plus space sin space straight x right parenthesis space sin space straight x space plus space left parenthesis cos space 3 straight x space minus space cos space straight x right parenthesis space cosx space equals space 0$

Find the principal solutions (0 ≤ x ≤ 2π ) of the following equation:

$cos space straight x space equals space minus fraction numerator 1 over denominator square root of 2 end fraction$

Find the principal solutions (0 ≤ x ≤ 2π ) of the following equation:

$space space space tan space straight x space equals space minus square root of 3$

Find the principal and general solutions of the following equation:

$sec space straight x space equals space 2$

Find the principal and general solutions of the following equation:

$cot space straight x space equals space minus square root of 3$

Find the principal and general solutions of the following equation:

$cosec space straight x space equals space minus 2$

Find the general solution of the following equation:

$sin space 2 straight x space equals space cos space straight x space$ .

Find the general solution of the following equation:

sin x + sin 3x + sin 5x = 0

Find the general solution of the following equation:

cos 3x + cos x - cos 2x = 0

Find the general solution of:

$2 space cos squared straight x space minus space 5 space cosx space plus space 2 space equals space 0$