Question

If $y={\tan }^{-1}\left[\frac{5\cos x-12\sin x}{12\cos x+5\sin x}\right]$ , then $\frac{dy}{dx}=$

• A. $1$
• B. $-1$
• C. $-2$
• D. $\frac{1}{2}$

Answer 1

The correct option is B $-1$

$y=ta{n}^{-1}\left[\frac{5cosx-12sinx}{12cosx+5sinx}\right]$

$y=ta{n}^{-1}\left[\frac{\frac{5}{12}-tanx}{1+\frac{5}{12}tanx}\right]$

Let $\frac{5}{12}=tanA$

$⟹y=ta{n}^{-1}\left[\frac{tanA-tanx}{1+tanAtanx}\right]$

$\therefore y=ta{n}^{-1}\left(tan\right(A-x\left)\right)$

$\therefore y=A-x$

$\therefore y^{{}^{\prime }}=-1$

Hence, the answer is option (B).