Chapter 1, Problem 12P

Two trigonometric identities are given by:

${\text{sin}}^{\text{5}}x\text{ = 5sin}x{\text{ – 20sin}}^{\text{3}}x{\text{ + 16sin}}^{\text{5}}x$ (b) ${\sin }^2{\cos }^{2}x=\frac{1\cos 4x}{8}$

For each part, verify that identify is corrected by calculating the value of the left and right sides of the equation, substituting $x=\frac{\pi }{12}$ .