(a) Find sin cos d. (b) You probably solved part (a) by making the substitution w = sin or w = cos

(a) Find ∫ sinθ cos θ dθ.
(b) You probably solved part (a) by making the substitution w = sin θ or w = cos θ. (If not, go back and do it that way.) Now find ∫ sin θ cos θ dθ by making the other substitution.
(c) There is yet another way of finding this integral which involves the trigonometric identities

sin(2θ) = 2 sin θ cos θ

cos(2θ) = cos² θ − sin² θ.

Find ∫ sinθ cos θ dθ using one of these identities and then the substitution w = 2θ.
(d) You should now have three different expressions for the indefinite integral ∫ sin θ cosθ dθ. Are they really different? Are they all correct? Explain.