Verify the identity

Problem:



Solution:

$\cot(\theta - \frac{\pi}{2})$

By definition of cotangent, we have

$= \frac{\cos(\theta - \frac{\pi}{2})}{\sin(\theta - \frac{\pi}{2})}$

By phase shift formulas, we have

$= \frac{\sin(\theta)}{-\cos(\theta)}$

By definition of tangent, we finally get

$= -\tan(\theta)$