Use the powerreducing formulas to rewrite the expression as

Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.

f(x)=11 sin^4 x

Solution

f(x)= 11sin⁴x

sin⁴x= (sin²x)²

sin²x= (1-cos2x)/2

therefore sin⁴x= ((1-cos2x)/2)²= (1+cos²2x-2cos2x)/4

And cos²2x= (1+ cos4x)/2

So we get 11sin⁴x= 11/4   + 11/8 +11 cos4x/8 -11 cos2x/2=33/8 + 11(cos4x)/8 -11(cos2x)/2