TextBook Solutions for Jharkhand Academic Council Class 12 Mathematics Mathematics Part I Chapter 2 Inverse Trigonometric Functions

Question 1

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Evaluates :

$open vertical bar table row cell straight a plus ib space space space space space straight c plus id end cell row cell negative straight c plus id space space space space space straight a minus ib space space space end cell end table close vertical bar$

Solution

Consider $open vertical bar table row cell straight a plus ib space space space space space straight c plus id end cell row cell negative straight c plus id space space space space space straight a minus ib space space space end cell end table close vertical bar$ = (a + i b) (a - i b)-(c + i b)(- c + i d)
= (a² - i²b²) - (i² d² - c²)
= (a² +b²) - (- d² - c²) [ $because$ i² = - 1 ]
= (a² +b² +c² + d²)

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TextBook Solutions for Jharkhand Academic Council Class 12 Mathematics Mathematics Part I Chapter 2 Inverse Trigonometric Functions

Evaluates :

$open vertical bar table row cell straight a plus ib space space space space space straight c plus id end cell row cell negative straight c plus id space space space space space straight a minus ib space space space end cell end table close vertical bar$

Evaluate

$open vertical bar table row cell 2 space space space space space 4 end cell row cell negative 1 space space space space 2 end cell end table close vertical bar$

Evaluate $open vertical bar table row 2 cell space space 4 end cell row cell negative 5 end cell cell negative 1 end cell end table close vertical bar$

Evaluate $open vertical bar table row straight x cell straight x plus 1 end cell row cell straight x minus 1 end cell straight x end table close vertical bar$

Evaluates :

$open vertical bar table row cell sin space 30 degree end cell cell cos space 30 degree end cell row cell negative sin space 60 degree end cell cell cos space 60 degree end cell end table close vertical bar$

Evaluate :

$open vertical bar table row cell 2 space cos space straight theta end cell cell negative 2 space sin space straight theta end cell row cell sin space straight theta end cell cell cos space straight theta end cell end table close vertical bar$

Evaluate

$open vertical bar table row cell cos space straight theta end cell cell negative space sin space straight theta end cell row cell sin space straight theta end cell cell cos space straight theta end cell end table close vertical bar$

Evaluate

$open vertical bar table row cell straight x squared minus straight x plus 1 end cell cell space space space space space straight x minus 1 end cell row cell straight x plus 1 end cell cell space space space space straight x plus 1 end cell end table close vertical bar$

If $A equals open square brackets table row 1 2 row 4 2 end table close square brackets$ then show that | 2A | = 4 | A |.

Find the values of each of the expressions.

$sin to the power of negative 1 end exponent open parentheses sin fraction numerator 2 straight pi over denominator 3 end fraction close parentheses$

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Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

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TextBook Solutions for Jharkhand Academic Council Class 12 Mathematics Mathematics Part I Chapter 2 Inverse Trigonometric Functions

Evaluates :

Evaluate

Evaluate

Evaluate

Evaluates :

Evaluate :

Evaluate

Evaluate

If then show that | 2A | = 4 | A |.

Find the values of each of the expressions.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Evaluates :

$open vertical bar table row cell straight a plus ib space space space space space straight c plus id end cell row cell negative straight c plus id space space space space space straight a minus ib space space space end cell end table close vertical bar$

Evaluate

$open vertical bar table row cell 2 space space space space space 4 end cell row cell negative 1 space space space space 2 end cell end table close vertical bar$

Evaluate $open vertical bar table row 2 cell space space 4 end cell row cell negative 5 end cell cell negative 1 end cell end table close vertical bar$

Evaluate $open vertical bar table row straight x cell straight x plus 1 end cell row cell straight x minus 1 end cell straight x end table close vertical bar$

Evaluates :

$open vertical bar table row cell sin space 30 degree end cell cell cos space 30 degree end cell row cell negative sin space 60 degree end cell cell cos space 60 degree end cell end table close vertical bar$

Evaluate :

$open vertical bar table row cell 2 space cos space straight theta end cell cell negative 2 space sin space straight theta end cell row cell sin space straight theta end cell cell cos space straight theta end cell end table close vertical bar$

Evaluate

$open vertical bar table row cell cos space straight theta end cell cell negative space sin space straight theta end cell row cell sin space straight theta end cell cell cos space straight theta end cell end table close vertical bar$

Evaluate

$open vertical bar table row cell straight x squared minus straight x plus 1 end cell cell space space space space space straight x minus 1 end cell row cell straight x plus 1 end cell cell space space space space straight x plus 1 end cell end table close vertical bar$

If $A equals open square brackets table row 1 2 row 4 2 end table close square brackets$ then show that | 2A | = 4 | A |.

Find the values of each of the expressions.

$sin to the power of negative 1 end exponent open parentheses sin fraction numerator 2 straight pi over denominator 3 end fraction close parentheses$