Chapter 6 - Analytic Trigonometry - Section 6.6 Double-angle and Half-angle Formulas - 6.6 Assess Your Understanding - Page 519: 43

$4cos^3\theta-3cos\theta$

$cos(3\theta)=cos(\theta+2\theta)=cos(\theta)cos(2\theta)-sin(\theta)sin(2\theta) =cos\theta(2cos^2\theta-1)-2sin^2\theta cos\theta =2cos^3\theta-cos\theta-2(1-cos^2\theta)cos\theta =2cos^3\theta-cos\theta-2cos\theta+2cos^3\theta =4cos^3\theta-3cos\theta$