Question

Use the power reducing formulas to rewrite the following identity in terms of the first power of cosine

Answer 1

Step by step explanation:

$\sin ^4(2x)=(\frac{1-\cos (2\cdot2x)}{2})^2$$\sin ^4(2x)=(\frac{1-\cos (4x)}{2})^2$$\sin ^4(2x)=\frac{1-2\cos(4x)+\cos^2(4x)}{4}$$\sin ^4(2x)=\frac{1-2\cos(4x)+\frac{1+\cos(8x)}{2}}{4}$$\sin ^4(2x)=\frac{\frac{2-4\cos (4x)+1+\cos (8x)}{2}}{4}$$\sin ^4(2x)=\frac{3-4\cos (4x)+\cos (8x)}{8}$$\sin ^4(2x)=\frac{3}{8}-\frac{\cos(4x)}{2}+\frac{\cos(8x)}{8}$$\sin ^4(2x)=\frac{3}{8}-\frac{1}{2}\cos (4x)+\frac{1}{8}\cos (8x)$