# How do you prove cos(x)tan(X) + sin(x)cot(x) = sin(x) + cos^2(x)?

Dec 20, 2015

Cannot be proven.

#### Explanation:

Know that: $\left\{\begin{matrix}\tan \left(x\right) = \sin \frac{x}{\cos} \left(x\right) \\ \cot \left(x\right) = \cos \frac{x}{\sin} \left(x\right)\end{matrix}\right.$

Thus,

$\cos \left(x\right) \tan \left(x\right) + \sin \left(x\right) \cot \left(x\right)$

$= \cos \frac{x}{1} \left(\sin \frac{x}{\cos} \left(x\right)\right) + \sin \frac{x}{1} \left(\cos \frac{x}{\sin} \left(x\right)\right)$

$= \sin \left(x\right) + \cos \left(x\right)$

Thus, the identity is invalid and cannot be proven.