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JEE Main202126 Feb 2021Morning ShiftMathematicsInverse Trigonometric FunctionsActual

If sin - 1 x a = cos - 1 x b = tan - 1 y c ; 0 < x < 1 , then the value of cos π c a + b is:

Options

  1. A1 - y 2 1 + y 2
  2. B1 - y 2
  3. C1 - y 2 y y
  4. D1 - y 2 2 y

Correct answer

A. 1 - y 2 1 + y 2

Step-by-step solution

sin - 1 x r = a , cos - 1 x r = b , tan - 1 y r = c So, a + b = π 2 r cos π c a + b = cos π tan - 1 y π 2 r r = cos 2 tan - 1 y , let tan - 1 y = θ = cos 2 θ = 1 - tan 2 θ 1 + tan 2 θ = 1 - y 2 1 + y 2

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