## Calculus, 10th Edition (Anton)

If we divide both sides of equality $f(x)\cos x=\sin x$ with $\cos(x)$ we get that $f(x)=\frac{\sin x}{\cos x}=\tan x$. Now it is easy to see that $$f'(x)=(\tan x)'=\sec^2x$$ So, the statement is true.