Trigonometry

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Question
SSCCGLENQA12042263

fraction numerator tan squared straight theta over denominator secθ plus 1 end fraction minus secθ is equal to
  • -1

  • 1

  • 0

  • None of these

Solution

A.

-1

We have,    fraction numerator tan squared straight theta over denominator secθ plus 1 end fraction minus secθ
           equals space fraction numerator sec squared straight theta minus 1 over denominator secθ plus 1 end fraction minus secθ
           equals space fraction numerator left parenthesis secθ plus 1 right parenthesis space left parenthesis secθ minus 1 right parenthesis over denominator left parenthesis secθ plus 1 right parenthesis end fraction minus secθ
           equals secθ minus 1 minus secθ equals negative 1
           

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Question
SSCCGLENQA12042264

sin to the power of 6 straight theta plus cos to the power of 6 straight theta is equal to 
  • 1 minus 3 sin squared θcos squared straight theta
  • 1 minus 3 sinθ space cosθ
  • 1 plus 3 sin squared θcos squared straight theta
  • 1

Solution

A.

1 minus 3 sin squared θcos squared straight theta

We have,  sin to the power of 6 straight theta space plus space cos to the power of 6 straight theta
               equals space left parenthesis sin squared straight theta right parenthesis cubed space plus space left parenthesis cos squared straight theta right parenthesis cubed
               equals left parenthesis sin squared straight theta plus cos squared straight theta right parenthesis space left square bracket sin to the power of 4 straight theta plus cos to the power of 4 straight theta minus sin squared θcos squared straight theta right square bracket
                open square brackets because space straight a cubed plus straight b cubed space equals space left parenthesis straight a plus straight b right parenthesis thin space left parenthesis straight a squared plus straight b squared minus ab right parenthesis close square brackets
               equals space left square bracket left parenthesis sin squared straight theta right parenthesis squared plus left parenthesis cos squared straight theta right parenthesis squared minus sin squared θcos squared straight theta right square bracket
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Question
SSCCGLENQA12042810

fraction numerator sinA over denominator 1 plus cosA end fraction space plus space fraction numerator sin begin display style straight A end style over denominator 1 minus cosA end fraction  left parenthesis 0 degree less than space straight A space less than space 90 degree right parenthesis is
  • 2 cosec A

  • 2 sec A

  • 2 sin A

  • 2 cos A

Solution

A.

2 cosec A

fraction numerator sinA over denominator 1 plus cosA end fraction plus fraction numerator sin begin display style straight A end style over denominator 1 minus cosA end fraction
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Question
SSCCGLENQA12042533

(1 + sec 20° + cot 70°)(1 - cosec 20° + tan70°) is equal to

  • 0

  • 1

  • 2

  • 3

Solution

C.

2

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Question
SSCCGLENQA12042613

a, b, c are the lengths of three sides of a triangle ABC. If a, b, c are related by the relation a2 + b2 + c2 = ab + bc + ca, then the value of sin2A+ sin2B + sin2C is

  • 3 over 4
  • fraction numerator 3 square root of 3 over denominator 2 end fraction
  • 3 over 2
  • 9 over 4

Solution

D.

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rightwards double arrow space space straight a squared plus straight b squared minus 2 ab space plus space straight b squared plus straight c squared minus 2 bc space plus space straight c squared space plus space straight a squared space minus space 2 ca space equals space 0
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Δ ABC is an equilateral triangle.
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4