The value of (1 + sec 20° + cot 70°) (1 - cosec 20&d

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 Multiple Choice QuestionsMultiple Choice Questions

121.

If straight x space equals space cosec space straight theta space minus space sin space straight theta and straight y equals space secθ space minus space cosθ, then the value of x2y2 (x2 + y2 + 3) is

  • 0

  • 1

  • 2

  • 3

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122.

The least value of (4 sec2θ +  9 cosec2θ) is

  • 1

  • 19

  • 25

  • 7

29 Views

123.

If 0 space less or equal than space straight theta space less or equal than space space straight pi over 2 comma space space 2 straight y space cos space straight theta space equals space straight x space sin space straight theta and 2 straight x space sec space straight theta space minus space straight y space cosec space straight theta space equals space 3 comma then the value of x2 + 4y2 is

  • 1

  • 2

  • 3

  • 4

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124.

If sin space 2 straight theta space equals space 1 half comma then the value of cos (75° - θ) is

  • 1 half

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

  • fraction numerator 1 over denominator square root of 2 end fraction

  • 1

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125.

If 0 space less or equal than space straight alpha space less or equal than space straight pi over 2 and 2 space sin space straight alpha space plus space 15 space cos squared straight alpha space equals space 7 comma then the value of cot space straight alpha is

  • 5 over 4

  • 3 over 4

  • 1 fourth

  • 1 half

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126.

If sin (x + y) = cos {3 (x + y)}, then the value of tan {2(x + y)} is

  • 1

  • 0

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

  • square root of 3

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127.

The value of 
(1 + sec 20° + cot 70°) (1 - cosec 20° + tan 70°) is

  • -1

  • 2

  • 1

  • 0


B.

2

(1 + sec 20° + cot 70°) (1 - cosec 20° + tan 70°)
equals space open curly brackets 1 plus space sec space left parenthesis 90 degree space minus space 70 degree right parenthesis space plus space cot space 70 degree right parenthesis close curly brackets space open curly brackets 1 space minus space cosec space left parenthesis 90 degree space minus space 70 degree right parenthesis plus space tan space 70 degree close curly brackets
equals space open curly brackets 1 space plus space cosec space 70 degree space plus space cot space 70 degree close curly brackets space open curly brackets 1 space minus space sec space 70 degree space plus space tan space 70 degree close curly brackets
equals space open square brackets 1 plus fraction numerator 1 over denominator sin space 70 degree end fraction space plus space fraction numerator cos space 70 degree over denominator sin space 70 degree end fraction close square brackets space open square brackets 1 minus fraction numerator 1 over denominator cos space 70 degree end fraction space plus space fraction numerator sin space 70 degree over denominator cos space 70 degree end fraction close square brackets
equals space fraction numerator left parenthesis sin space 70 degree space plus space cos space 70 degree plus 1 right parenthesis thin space left parenthesis sin space 70 degree space plus space cos space 70 degree space minus space 1 right parenthesis over denominator sin space 70 degree space cos space 70 degree end fraction
equals space fraction numerator sin squared 70 degree space plus space cos squared 70 degree space plus space 2 space sin space 70 degree space cos space 70 degree space minus space 1 over denominator sin space 70 degree space cos space 70 degree end fraction
equals space fraction numerator 2 space sin space 70 degree space cos space 70 degree over denominator sin space 70 degree space cos space 70 degree end fraction space space open square brackets because sin squared 70 degree space plus space cos squared 70 degree space equals space 1 close square brackets
equals space space space 2

 

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128.

If x sin3θ + y cos3θ = sin θ cos θ ≠ 0
and x sin θ  - y cos θ = 0,   then the value of (x2 + y2) is

  • sin θ - cos θ

  • sin θ + cos θ

  • 0

  • 1

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129.

If straight mu subscript straight n space equals space cos to the power of straight n straight alpha space plus space sin to the power of straight n straight alpha comma then the value of 2 straight mu subscript 6 space minus space 3 straight mu subscript 4 space plus space 1 is

  • 4

  • 6

  • 0

  • 1

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130.

If sec θ - cosec θ = 0,  then the value of (sec θ + cosec θ)

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

  • 0

  • 2 square root of 2

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

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