(1 + sin α) (1 + sin β) (1 + sin γ) = (1 - sin &

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 Multiple Choice QuestionsMultiple Choice Questions

141.

If a sin θ + b cos θ = c, then the value of a cos θ - b sin sin θ is

  • plus-or-minus space square root of straight a squared minus straight b squared minus straight c squared end root

  • plus-or-minus space square root of straight a squared minus straight b squared plus straight c squared end root

  • plus-or-minus space square root of negative straight a squared space plus space straight b squared space plus space straight c squared end root

  • plus-or-minus space square root of straight a squared plus straight b squared minus straight c squared end root

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142.

If cosx + cos2x = 1, then the numerical value of (sin12x + 3 sin10x + 3 sin8x + sin6x - 1) is

  • 0

  • 1

  • -1

  • 2

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143.

If sin space left parenthesis straight A minus straight B right parenthesis space equals space 1 half and cos space left parenthesis straight A space plus space straight B right parenthesis space equals space 1 half comma where A > B > 0 and A + B is an acute angle, then the value of B is

  • straight pi over 6

  • straight pi over 12

  • straight pi over 4

  • straight pi over 2

34 Views

144.

Maximum value of (2 sin θ + 3 cos θ) is

  • 2

  • square root of 13

  • square root of 15

  • 1

31 Views

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145.

The value of 152 (sin 30° + 2 cos2 45° + 3 sin 30° + 4 cos2 45° +...+17 sin 30° + 18 cos45°) is

  • an integer but not a perfect square

  • a rational number but not an integer

  • a perfect square of an integer

  • irrational

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146.

(1 + sin α) (1 + sin β) (1 + sin γ) = (1 - sin α) (1 - sin β) (1 - sin γ), then each side is equal to

  • plus-or-minus space cos space straight alpha. space cos space straight beta. space cos space straight gamma

  • plus-or-minus space space sin space straight alpha space sin space straight beta space space sin space straight gamma

  • plus-or-minus space space sin space straight alpha space space cos space straight beta space space cos space straight gamma

  • plus-or-minus space sin space straight alpha space space sin space straight beta space space cos space straight gamma


A.

plus-or-minus space cos space straight alpha. space cos space straight beta. space cos space straight gamma

Let (1 + sin α) (1 + sin β) (1 + sin γ) = (1 - sin α) (1 - sin β) (1 - sin γ) = x.
∴  x. x  = (1 + sin α) (1 + sin β) (1 + sin γ) (1 - sin α) (1 - sin β) (1 - sin γ) 
  x2 = (1 - sin2α) (1 - sin2β) (1 - sin2γ)
  x2 = cos2α . cos2β . cos2γ
  straight x space equals space plus-or-minus space cos space straight alpha. space cos space straight beta. space cos space straight gamma

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147.

If sin θ + sin θ = 1, then cos2 θ + cos4 θ is equal to

  • 1

  • fraction numerator cos squared straight theta over denominator sinθ end fraction

  • fraction numerator sin space straight theta over denominator cos to the power of 2 space end exponent straight theta end fraction

  • None


148.

The maximum value of sin4 θ + cos4 θ is

  • 2

  • 1

  • 3

  • 1 third


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149.

The numerical value of 
fraction numerator cos squared space 45 degree over denominator sin squared space 60 degree end fraction space plus space fraction numerator begin display style cos squared space 60 degree end style over denominator begin display style sin squared space 45 degree end style end fraction space minus space fraction numerator begin display style tan squared space 30 degree end style over denominator begin display style cot squared space 45 degree end style end fraction space minus space fraction numerator begin display style sin squared end style begin display style space end style begin display style 30 end style begin display style degree end style over denominator cot squared space 30 degree end fraction

  • 3 over 4

  • 1 fourth

  • 1 half

  • 1 1 fourth


150.

Find the value of tan 4° tan 43° tan 47° tan 86°.

  • 1

  • 2 over 3

  • 1 half

  • 2


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