Use the powerreducing formulas as many times as possible to

Use the power-reducing formulas as many times as possible to rewrite the expression in terms of the first power of the cosine. 4 * sin^4 (2x)

Solution

4 * sin^4 (2x)

4sin^2(2x)sin^2(2x)

2sin^2(2x)*2sin^2(2x)

use the formula:cos2x =1- 2sin^2x

= ( 1- cos4x)(1-cos4x)

= 1 - cos4x -cos4x +cos^2(4x)

= 1 - 2cos4x +cos^2(4x)

again use the formul: cos2x = 2cos^2(4x) -1

= 1- 2cos4x + (1 +cos8x)/2

= 3/2 - 2cos4x + cos8x/2