3. Solve the equation $\cos 17 x=20 \cos x$.

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However, since the equation itself is already in a universal mathematical notation, the translation of the problem statement is as follows:

3. Solve the equation $\cos 17 x=20 \cos x$.
3. Let $x=\pi / 2-y$, then $\cos x=\sin y, \cos 17 x=\sin (17 \pi / 2-17 y)=\sin 17 y$. Therefore, $\sin 17 y=20 \sin y$. It is easy to see that $|\sin n y| \leqslant n|\sin y|$ for natural $n$. This inequality is proved by induction: for $n=1$ it is obvious, and further $|\sin (n+1) y|=|\sin n y \cos y+\sin y \cos n y| \leqslant|\sin n y|+|\sin y| \leqslant(n+1)|\sin y|$ by the induction hypothesis. So the equality holds only when $\sin y=0$, that is, $y=\pi k, x=\pi / 2-\pi k, k \in \mathbb{Z}$.