sin(2x) = 2sin(x)cos(x). Substitute and solve for x.

There will be four solutions.

$\text{sin}(x+\pi )+\text{cos}\left(x-\frac{\pi}{2}\right)=-\text{sin}(x)+\text{cos}(x)\text{cos}\left(\frac{\pi}{2}\right)+\text{sin}(x)\text{sin}\left ( \frac{\pi}{2} \right )$

There is no solution to this problem.

$\text{cot}(x)=\frac{\text{cos}(x)}{\text{sin}(x)}\ \ \ \ \ \text{tan}(x)=\frac{\text{sin}(x)}{\text{cos}(x)}$

There will be four solutions.