cos²x - sin²x = cos2x +sin²x
hm you see I created this identity.. it's a class assignment and we have to see if someone can prove it?
I started off with cos²x = cos²x
and from there you're supposed to keep replacing terms with equivalent equations to make it complex.
Im trying to see if it makes sence and if its possible to prove..
$\displaystyle \cos(2x) + \sin^2(x) = \cos^2(x) - \sin^2(x)$
Set $\displaystyle x = \frac{\pi}{2}$.
$\displaystyle \cos(\pi) + \sin^2(\pi/2) = -1 + 1 = 0 $
But
$\displaystyle \cos^2(\pi/2) - \sin^2(\pi/2) = 0 - 1^2 = -1$.
Not the same thing am afraid.
Show me how you got it and I'll show you where you went wrong...