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) $