Question

If $y=\sin x^0$ and $z=\cos x$ then $\frac{dy}{dz}$ is equal to

• A. $-cosecx.\cos x$
• B. $\frac{\pi }{180}cosec\frac{\pi x}{180}.\cos x$
• C. $-\frac{\pi }{180}cosecx.\cos \frac{\pi x}{180}$
• D. none of these

Answer 1

Answer: (C)

$-\frac{\pi }{180}cosecx.\cos \frac{\pi x}{180}$

$y=\sin x^0\Rightarrow \frac{dy}{dx}=\cos x^0\times \frac{\pi }{180}$

$z=\cos x\Rightarrow \frac{dz}{dx}=-\sin x$

$\therefore \frac{dy}{dz}=\frac{\frac{\pi }{180}\cos x^0}{-\sin x}=-\frac{\pi }{180}\csc x\cos x^0$

$=-\frac{\pi }{180}\csc x\cos \left(\frac{\pi x}{180}\right)$