Chapter 1, Problem 11P

Two trigonometric identities are given by:

(a) ${\left(\text{sin }x+\text{cos }x\right)}^2=1+2\text{sin }x\text{cos }x$

(b) $\frac{1-2\text{ cos }x-3{\text{cos}}^{2}x }{{\text{sin}}^{2}x}=\frac{1-3\text{cos }x}{1-\text{cos }x}$

For each part, verify that the identity is correct by calculating the values of the left and right sides of the equation, substituting $x=\text{2}0°$ .