(a)[3]
Prove the identity $\sin 4x = 4\sin x\left(2\cos^3 x-\cos x\right)$.
(b)[5]
Hence find the exact value of the integral $\int_{0}^{\frac{\pi}{4}} \cos^3 x\sin 4x\,dx$.
Mathematics 9709 · AS & A Level · Trigonometry
Mathematics 9709 · AS & A Level · Trigonometry
Prove the identity $\sin 4x = 4\sin x\left(2\cos^3 x-\cos x\right)$.
Hence find the exact value of the integral $\int_{0}^{\frac{\pi}{4}} \cos^3 x\sin 4x\,dx$.