If  and , then the value of x2y2 (x2 + y2 + 3) is

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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

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straight x squared space space plus space space straight y squared space plus space 3 space equals space left parenthesis cosec space straight theta space space minus space sin space straight theta right parenthesis squared space plus space left parenthesis sec space straight theta space minus space cos space straight theta right parenthesis squared space plus space 3
                equals space cosec squared straight theta space plus space sec squared straight theta space minus space 3 space plus space 3 space space equals space fraction numerator 1 over denominator sin squared straight theta space cos squared straight theta end fraction
        straight x squared straight y squared space equals space left parenthesis cosec space straight theta space minus space sin space straight theta right parenthesis squared space left parenthesis sec space straight theta space minus space cos space straight theta right parenthesis squared
space space space space space space space equals space open parentheses fraction numerator 1 over denominator sin space straight theta end fraction space minus space sin space straight theta close parentheses squared space open parentheses fraction numerator 1 over denominator cos space straight theta end fraction space minus space cos space straight theta close parentheses squared
space space space space space space space equals space open square brackets fraction numerator 1 minus sin squared straight theta over denominator sinθ end fraction. space fraction numerator 1 minus cos squared straight theta over denominator cosθ end fraction close square brackets squared space
space space space space space space space equals space open square brackets fraction numerator cos squared straight theta space sin squared straight theta over denominator sin space straight theta. space cos space straight theta end fraction close square brackets squared
space space space space space space space equals space cos squared straight theta space space sin squared straight theta

therefore space space space space straight x squared straight y squared left parenthesis straight x squared space plus space straight y squared plus 3 right parenthesis space equals space fraction numerator 1 over denominator sin squared θcos squared straight theta end fraction space. space cos squared straight theta space sin squared straight theta space equals space 1

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122.

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

  • 1

  • 19

  • 25

  • 7

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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

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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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