The derivative of tan^-1 ( sinx- cosx sinx+ cosx ), with respect to x2, where (x ∈ (0 , 2 ) ) is :

Question

Accepted Answer

Correct answer: D. (d) JEEN Main 2019 f (x )= tan^-1 ( tanx-1 tanx+1 ) =- tan^-1 ( tan( 4-x) ) ( ∵ 4-x ∈(- 4 , 4)) So, f (x )=-( 4-x)=x- 4 Let y= x2 ⇒f (y )=2y- 4 Now, differentiate w.r.t y , df (y ) dy=2.

$The derivative of tan^{- 1} (\frac{sin x - cos x}{sin x + cos x}), with respect to \frac{x}{2}, where (x \in (0, \frac{π}{2})) is :$

Solution

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