Chapter 1, Problem 10P

Two trigonometric identities are given by:

(a) ${\text{cos}}^{2}x-{\text{sin}}^{2}x=1-2{\text{sin}}^{2}x$

(b) $\frac{\text{tan }x}{\text{sin }x-2 \text{tan }x}=\frac{1}{\text{cos }x-2}$

For each part, verify that the identity is correct by calculating the left and right sides of the equation, substituing $x=\pi /\text{1}0$ .