If  then  is from Quantitative Aptitude Trig

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 Multiple Choice QuestionsMultiple Choice Questions

131.

If straight P space sin space straight theta space equals space square root of 3 and P cosθ = 1,  then the value of P is

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

  • negative fraction numerator 1 over denominator square root of 3 end fraction

  • 2

  • 1 half

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132.

The value of fraction numerator 1 over denominator left parenthesis 1 plus tan squared straight theta right parenthesis end fraction space plus space fraction numerator 1 over denominator left parenthesis 1 plus cot squared straight theta right parenthesis end fraction is

  • 1

  • 2

  • 1 half

  • 1 fourth

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133.

If tan space straight theta space equals space 3 over 4 and θ is acute,  then cosec θ is equal to

  • 5 over 3

  • 5 over 4

  • 4 over 3

  • 4 over 5

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134.

If cos space straight theta space plus space sin space straight theta space equals space square root of 2 space cos space straight theta comma then cos θ - sin θ is

  • negative square root of 2 space cos space straight theta

  • negative square root of 2 space sin space straight theta

  • square root of 2 space sin space straight theta

  • square root of 2 space tan space straight theta

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135.

The value of fraction numerator 1 over denominator cosec space straight theta space minus space cot space straight theta end fraction space minus space fraction numerator 1 over denominator sin begin display style space end style begin display style straight theta end style end fraction is

  • cot θ

  • cosec θ

  • tan θ

  • 1

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136.

If cos to the power of 4 straight theta space minus space sin to the power of 4 straight theta space equals space 2 over 3 comma space then the value of 1 - 2 sin2θ  is

  • 0

  • 2 over 3

  • 1 third

  • 4 over 3

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137.

If tan space straight alpha space equals space straight n space space tan space straight beta space space and space sin space αθ space equals space straight m space sin space straight beta comma space space then cos squared straight alpha is

  • straight m squared over straight n squared

  • fraction numerator straight m squared minus 1 over denominator straight n squared minus 1 end fraction

  • fraction numerator straight m squared plus 1 over denominator straight n squared plus 1 end fraction

  • fraction numerator straight m squared over denominator straight n squared plus 1 end fraction


B.

fraction numerator straight m squared minus 1 over denominator straight n squared minus 1 end fraction

space space tan space straight alpha space equals space straight n space tan space straight beta
space space fraction numerator sin space straight alpha over denominator cos space straight alpha end fraction space equals space fraction numerator straight n space sin space straight beta over denominator cos space straight beta end fraction
                     [As sin space straight alpha space equals space straight m space sin space straight beta]
therefore space space space fraction numerator straight m space sin space straight beta over denominator cos space straight alpha end fraction space equals space fraction numerator straight n space sin space straight beta over denominator cos space straight beta end fraction
rightwards double arrow space space space space straight m space cos space straight beta space equals space straight n space cos space straight alpha space space space space space space space... left parenthesis straight i right parenthesis space
straight m space sin space straight beta space equals space sin space straight alpha space space space left parenthesis given right parenthesis space space space space... left parenthesis ii right parenthesis
Squaring and Adding (i) and (ii), we get,
rightwards double arrow space space straight m squared space cos squared straight beta space plus space straight m squared space sin squared straight beta space equals space straight n squared space cos squared straight alpha space plus space sin squared straight alpha
rightwards double arrow space space straight m squared left parenthesis cos squared straight beta space space plus space sin squared straight beta right parenthesis space equals space straight n squared cos squared straight alpha space plus space left parenthesis 1 minus cos squared straight alpha right parenthesis
rightwards double arrow space space straight m squared space equals space straight n squared cos squared straight alpha space plus space 1 minus cos squared straight alpha
rightwards double arrow space space straight m squared space minus space 1 space equals space cos squared straight alpha left parenthesis straight n squared minus 1 right parenthesis
rightwards double arrow space space space cos squared straight alpha space equals space fraction numerator straight m squared minus 1 over denominator straight n squared minus 1 end fraction

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138.

The value of (tan 1°  tan 2°  tan 3°.... tan 89°) is

  • undefined

  • 0

  • 1

  • 89

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139.

If straight x space equals space straight a space sec space straight theta space cos space straight ϕ comma space space straight y space equals space straight b space sec space straight theta space sin space straight ϕ and straight z space equals space straight c space tan space straight theta. then the value of straight x squared over straight a squared space plus space straight y squared over straight b squared space equals space straight z squared over straight c squared

  • 9

  • 0

  • 1

  • 4

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140.

If fraction numerator sec space straight theta space plus space tan space straight theta over denominator sec space straight theta space minus space tan space straight theta end fraction space equals space 5 over 3 comma then sin θ is equal to

  • 2/3

  • 3/4

  • 1/4

  • 1/3

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