99 Percentile Qs Bank for JEE MainMathematicsDifferentiation

If x = 1 - t 2 1 + t 2 and y = 2 t 1 + t 2 , t h e n d y d x is equal to

Options

A- y x
By x
C- x y
Dx y

Correct answer

C. - x y

Step-by-step solution

∵ x = 1 - t 2 1 + t 2 a n d y = 2 t 1 + t 2 Put t = tan ⁡ θ in both the equations, we get x = 1 - tan 2 ⁡ θ 1 + tan 2 ⁡ θ = cos ⁡ 2 θ ...(i) and y = 2 tan ⁡ θ 1 + tan 2 ⁡ θ = sin ⁡ 2 θ ...(ii) On differentiating both the eqs.(i) and (ii), we get d x d θ = - 2 sin ⁡ 2 θ a n d d y d θ = 2 cos ⁡ 2 θ Therefore, d y d x = d y d θ d x d θ = - cos ⁡ 2 θ sin ⁡ 2 θ = - x y

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