Chapter 7 - Section 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas - 7.3 Exercises - Page 561: 32

a. $\cos \theta$ b. $\sin \theta$

a. Use the formula $\cos 2x=\cos^2 x-\sin^2 x$ with $x=\frac{\theta}{2}$. Then $\cos^2 \frac{\theta}{2}-\sin^2\frac{\theta}{2}=\cos(2*\frac{\theta}{2})=\cos \theta$. b. Use the formula $\sin 2x=2\sin x\cos x$ with $x=\frac{\theta}{2}$. Then $2\sin \frac{\theta}{2}\cos \frac{\theta}{2}=\sin(2*\frac{\theta}{2})=\sin \theta$.