Question

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

Answer 1

This is not a valid identity.

Explanation:

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

`cos x * sin x = 1 * 0 = 0`

`cos x + sin x = 1 + 0 = 1`

So `cos x * sin x != 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]}