sin^2(x)/1 + cos(x) = 1 - cos(x)
We know that sin^2 x = 1 - cos^2 x. It is one of our trig identities.
We now have this:
(1 - cos^2 x)/(1 + cos x) = 1 - cos x
Take note:
1 - cos^2 x is a perfect square difference in terms of cosine.
So, (1 - cos^2 x) = (1 + cos x)(1 - cos x).
We now have this:
[(1 + cos x)(1 - cos x)]/(1 + cos x) = 1 - cos x
Do you see what happens on theft side?
On the left side, (1 + cos x) cancels out on the top and bottom.
We are now left with this:
1 - cos x = 1 - cos x
Done!!
