Let (x) = sin 2 x and g(x) = cos 2 x. (a) Use an identity and prove '(x) = g'(x) without directly computing '(x)

Let ƒ(x) = sin² x and g(x) = cos² x.
(a) Use an identity and prove ƒ'(x) = −g'(x) without directly computing ƒ'(x) and g'(x).
(b) Now verify the result in (a) by directly computing ƒ'(x) and g'(x).