+322 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
+130077 4 sin^4 (2x)
[2sin^2 (2x)]^2 =
4 [sin^2(2x)]^2 =
4 [ (1 - cos (4x) ) / 2 ]^2 =
[ 1 - cos (4x) ] ^2 =
1 - 2cos(4x) + cos^2(4x) =
1 - 2cos(4x) + [ 1 - cos (8x)] / 2 =
1 - 2 cos (4x) + (1/2) - (1/2)cos(8x) =
(1/2) [ 2 - 4cos(4x) + 1 - cos(8x) ] =
(1/2) [ 3 - 4cos(4x) - cos(8x) ]
