# How do you prove:  cosx*sinx=cosx+sinx?

##### 1 Answer
Feb 12, 2016

This is not a valid identity.

#### Explanation:

For example, with $x = 0$ we find:

$\cos x \cdot \sin x = 1 \cdot 0 = 0$

$\cos x + \sin x = 1 + 0 = 1$

So $\cos x \cdot \sin x \ne \cos x + \sin x$

Here are graphs of the functions corresponding to the two sides of the equation:
graph{(y-cos x * sin x)(y - cos x - sin x) = 0 [-5, 5, -2.5, 2.5]}