An equation like sin 2 + cos 2 = 1 is called an identity because

An equation like sin² θ + cos² θ = 1 is called an identity because it holds for all values of θ. An equation like sin θ = 0.5 is not an identity because it holds only for selected values of θ, not all. If you differentiate both sides of a trigonometric identity in θ with respect to θ, the resulting new equation will also be an identity.

Differentiate the following to show that the resulting equations hold for all θ.

a. sin 2θ = 2sin θ cos θ

b. cos 2θ = cos2 θ - sin2 θ