15. $\log _{\cos x} \sin x-2 \log _{\sin x} \cos x+1=0$.
15. Transition to logarithms with base $\cos x, x \neq 0, x \neq \frac{\pi}{2}$ $\left(\log _{\cos x} x \sin x\right)^{2}+\log _{\cos x} \sin x-2=0, \quad \log _{\cos x} \sin x=1$.

From where $x_{1}=\frac{\pi}{4}+\pi k$. The roots of the equation $\log _{\cos } x \sin x=-2$ are extraneous.