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JEE Main2018MathematicsDifferentiationActual

If x = 2 cosec - 1 t and y = 2 sec - 1 t , t ≥ 1 , then d y d x is equal to

Options

  1. Ay x
  2. B- y x
  3. C- x y
  4. Dx y

Correct answer

B. - y x

Step-by-step solution

Given, x = 2 cosec - 1 t = 2 cosec - 1 t 2 and y = 2 sec - 1 t = 2 sec - 1 t 2 , then we have x · y = 2 sec − 1 t + cosec − 1 t 2 And, we know that sec - 1 x + cosec - 1 x = π 2 , ⇒ x y = 2 π 4 On differentiating, both sides with respect to x , and applying product rule, we get x d y d x + y = 0 ⇒ d y d x = - y x .

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