Question

If $y =f\left(x\right)=-cosec\, x\cdot cos\,x$, then $\left(\frac{dy}{dx}\right)_{x=\frac{\pi}{2}}$ is equal to

• A. $0$
• B. $\frac{1}{2}$
• C. $1$
• D. $3$

Answer 1

Answer: (C)

We have, $y = -cosec\, x \,cos \,x$
$\Rightarrow y=-\frac{cos\,x}{sin\,x}=-cot\,x$
$\therefore \frac{dy}{dx}=-\left(-cosec^{2}\,x\right)=cosec^{2}\,x$
$\therefore \frac{dy}{dx}\bigg|_{at\,x=\frac{\pi}{2}}$$=\left(cosec \frac{\pi}{2}\right)^{2}=\left(1\right)^{2}=1$