Question

how do I prove these two identities..?
1. sin x(cos x cot x – sin x) = cos (2x)
2. 1 + cos (8x) = 2 cos2(4x)

Answer 1

try distributing the sin(x) for the first one. (some factor depending if you wrote in terms of cos(x) and sin(x) should "cancel")

Answer 2

I bet that one two is an exponent in the second
since 4x is half of 8x
I would think double angle identity

Answer 3

Okay.