If x = sin 3 θ cos 2 θ and y = cos 3 θ sin 2 θ , where sin θ + cos θ = 1 2 , then x + y =

Step-by-step solution

It is given that x = sin 3 θ cos 2 θ y = cos 3 θ sin 2 θ The summation of   x and   y is x + y = sin 3 θ cos 2 θ + cos 3 θ sin 2 θ = sin θ 1 - cos 2 θ cos 2 θ + cos θ 1 - sin 2 θ sin 2 θ = sin θ 1 cos 2 θ - 1 + cos θ 1 sin 2 θ - 1 = sin θ cos 2 θ + cos θ sin 2 θ - ( sin θ + cos θ ) = sin θ cos 2 θ + cos θ sin 2 θ - 1 2 = sin 3 θ + cos 3 θ cos 2 θ sin 2