Write the derivative of sin x with respect to cos x.

We have to find $\frac{d}{d(\cos x)}(\sin x)$

So, we use the Chain Rule of Differentiation to evaluate this.

$\frac{d}{d(\cos x)}(\sin x)=\frac{d(\sin x)}{d x} \cdot \frac{d x}{d(\cos x)}$

$=\cos x \cdot \frac{1}{-\sin x}$

$=-\cot x($ Ans $)$