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TS EAMCET · Maths · Differentiation

If \(y=\tan ^{-1}\left[\frac{5 \cos x-12 \sin x}{12 \cos x+5 \sin x}\right]\), then \(\frac{d y}{d x}\) is equal to

  1. A 1
  2. B -1
  3. C -2
  4. D \(\frac{1}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(B) -1

Step-by-step Solution

Detailed explanation

Given, \[ \begin{aligned} y & =\tan ^{-1}\left[\frac{5 \cos x-12 \sin x}{12 \cos x+5 \sin x}\right] \\ & =\tan ^{-1}\left[\frac{\frac{5}{12}-\tan x}{1+\frac{5}{12} \tan x}\right] \end{aligned} \] [divide by \(12 \cos x\) in denominator and numerator]…