Power-Reduction

Question

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

17sin⁴x

Answer 1

sin⁴x = (sin²x)(sin²x) = (1/4)(1-cos2x)(1-cos2x) = (1/4)(1 -2cos2x + cos²(2x))

= (1/4)(1 - 2cos2x + 1/2 + (1/2)cos4x) = (1/4)(3/2 - 2cos2x + cos4x/2)

So, 17sin4x = (17/4)(3/2 -2cos2x + cos4x/2)