Chapter 7 - Trigonometric Identities and Equations - Summary Exercises Verifying Trigonometric Identities - Exercises - Page 696: 16

See explanations.

1. Start from right side and use the identity $sec(x)=\frac{1}{cos(x)}$, we have $RHS=\frac{2-(\frac{1}{cos(x)})^2}{(\frac{1}{cos(x)})^2}=\frac{2(cos(x))^2-1}{1}=2cos^2(x)-1$ 2. Use the identify for $cos(2x)$, we have $LHS=cos(2x)=2cos^2(x)-1$ 3. As $LHS=RHS$, we proved the original identify.