Question

Rate of change of $sinx$ with respect to $cosx$ at $x=\frac{\pi }{2}$ will be equal to

• A. 0.0
• B. 1
• C. -1
• D. $-\infty$

Answer 1

The correct option is A 0.0

Rate of change of sinx with respect to cos x is the derivative of sin x with respect to cos x i.e. $\frac{d\left(sinx\right)}{d\left(cosx\right)}$
$\frac{d\left(sinx\right)}{d\left(cosx\right)}=\frac{\frac{d}{dx}\left(sinx\right)}{\frac{d}{dx}\left(cosx\right)}=\frac{cosx}{-sinx}=-cotx$
At $x=\frac{\pi }{2},cotx=0,$ which is the correct answer.