Trigonometric Function

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

sin^2 = (1 - cos2x)/2

cos^2 = (1 + cos2x)2

So then

sin^4 = (1-cos2x)^2/4

(1 - 2cos2x + cos^2(2x) ) / 4

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

(2 - 2 cos2x + cos(4x))/4

Answer 2

17sin⁴x Reduce to sin²x

17(sin²x)(sin²x) Substitute in power reducing formula for sin²x

17[(1-cos 2x)/2][(1-cos 2x)/2]