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

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Answer 1 · 2016-02-12T16:38:47

This is not a valid identity.

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]}

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