Porisma

A hint to get started

Apply the double-angle formula twice

Using cos⁡2A=2cos⁡2A−1\cos2A=2\cos^2A-1, show that cos⁡4x=38+12cos⁡2x+18cos⁡4x\cos^4x=\frac38+\frac12\cos2x+\frac18\cos4x. Hence find ∫cos⁡4x dx\int\cos^4x\,dx.

CJC · Lecture · Example 13

Use double angle first for cos squared x, then for cos squared 2x, as the source callouts specify.

Read the worked solution