Calculus homework

Question

F(0) = sin(0) cos(0) find the derivative

Answer 1

F(θ) = sinθcosθ

Recall that sin(2θ) = 2sinθcosθ. So, sinθcosθ = (1/2)sin(2θ).

Therefore, F'(θ) = (1/2)cos(2θ)(2) = cos(2θ) [or equivalently, cos²θ - sin²θ ]