Prove the following identities

1. $\displaystyle \sin (\Pi + x) + \cos ( \frac{\Pi}{2} - x) + \tan (\frac{\Pi}{2} + x) = -\cot x$

2. $\displaystyle \frac{\sin (4x) - \sin (2x)}{\sin (2x)} = \frac{\cos (3x)}{\cos (x)}$

3. $\displaystyle \cos (x) + \cos (2x) + \cos (3x) = \cos (2x) (1+ 2 \cos (x)) $

Solve

1. $\displaystyle \cos^2 (2x) + 2 \cos (2x) + 1 = 0 [-\Pi , \Pi] $

2. $\displaystyle \tan (4x) - \tan (2x) = 0 [0,\Pi] $

These are the ones I couldn't solve from a worksheet I got in class. Please help