Use the power reduction formulas to rewrite the expression 9

Use the power reduction formulas to rewrite the expression. 9 sin^2(x) cos^2(x)

Solution

9sin²xcos²x

9(1-cos²x)cos²x

9(cos²x-cos⁴x)

9((cos 2x +1)/2 - ( (cos2x +1)/2)^2)

9((cos2x+1)/2 - (cos²2x +1 +2cos2x)/4)

9((cos 2x +1)/2 - ((cos4x +1)/2 +1 +2 cos 2x)/4)

9/8(1-cos(4x))