posted by Melody .
Are any of these three problems identities?
If so, how can you conclude that any of them are identities?
Yes. You can prove an identity by rearranging one side of the equation to match the other.
cos^2(x) - sin^2(x) = 1 - sin^2(x) - sin^2(x) because cos^2(x) + sin^2(x) = 1
= 1 - 2 sin^2(x)
The second one is not an identity. You can prove this by substituting the appropriate sin/cos functions for sec(x) and csc(x).