Question

If $y={\tan }^{-1}\left(\cot (\frac{\pi }{2}-x)\right),$ then $\frac{dy}{dx}=$

• A. $1$
• B. $-1$
• C. $0$
• D. $\frac{1}{2}$

Answer 1

Answer: (A)

$1$

$y={\tan }^{-1}\left(\cot (\pi /2-x)\right)$

$\Rightarrow y={\tan }^{-1}\left(tanx\right)=x$

$\therefore$ $\frac{dy}{dx}=1$ [A]