#### Answer

The statement is true.

#### Work Step by Step

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.