Question

How do you prove `sin(a+b)cos(a+b) = (sina)^2 - (sinb)^2`?

Answer 1

The given identity is not true.

Explanation:

Take `a = pi/2` and `b = 0`

Then

`sin(a+b)cos(a+b) = sin(pi/2)cos(pi/2) = 1*0 = 0`

but

`sin^2(a)-sin^2(b) = sin^2(pi/2)-sin^2(0) = 1^2 - 0^2 = 1`

thus the left hand side and right hand side do not always match, and so the identity is not correct.