(i)[5]
Show that $\cos 3x = 4\cos^3 x - 3\cos x$ by expanding $\cos(2x + x)$ first.
(ii)[5]
Hence show that $\displaystyle \int_{0}^{\frac{1}{6}\pi} (2\cos^3 x - \cos x)\,dx = \frac{5}{12}$.
Mathematics 9709 · AS & A Level · Integration
Mathematics 9709 · AS & A Level · Integration
Show that $\cos 3x = 4\cos^3 x - 3\cos x$ by expanding $\cos(2x + x)$ first.
Hence show that $\displaystyle \int_{0}^{\frac{1}{6}\pi} (2\cos^3 x - \cos x)\,dx = \frac{5}{12}$.