2. (7 points) Provide an example of a number $x$ for which the equality $\sin 2017 x - \operatorname{tg} 2016 x = \cos 2015 x$ holds. Justify your answer.
Answer. For example, $\frac{\pi}{4}$.

Solution. Since $\frac{2016 \pi}{4}=504 \pi=252 \cdot 2 \pi$ is a multiple of the period, we have

$$
\begin{gathered}
\sin \frac{2017 \pi}{4}=\sin \left(252 \cdot 2 \pi+\frac{\pi}{4}\right)=\sin \frac{\pi}{4}=\frac{\sqrt{2}}{2} \\
\cos \frac{2015 \pi}{4}=\cos \left(252 \cdot 2 \pi-\frac{\pi}{4}\right)=\cos \left(-\frac{\pi}{4}\right)=\frac{\sqrt{2}}{2} \\
\operatorname{tg} \frac{2016 \pi}{4}=\operatorname{tg}(252 \cdot 2 \pi)=\operatorname{tg} 0=0 \\
\frac{\sqrt{2}}{2}-0=\frac{\sqrt{2}}{2}
\end{gathered}
$$

## Grading Criteria.

- The correct answer is provided, and it is shown that the equality holds for this value of $x$, -7 points.
- The correct answer is provided only - 3 points.