Question

Rewrite the expression in terms of the first power of the cosine

sin^8(x)

how do i do this plz help !!

Answer 1

I can get it in powers of cos but not first power

sin^8 = sin^2 * sin^2 *sin^2 *sin^2
but
sin^2 = 1 - cos^2
sin^2*sin^2 = 1-2cos^2+cos^4

(1-2cos^2+cos^4)^2
= 1-4cos^2x+6cos^4x-4cos^6x+cos^8x

Answer 2

recall that cos^2 x = (1+cos2x)/2
so, cos^4 x = (1+cos2x)^2/4 now cos^2 2x = (1+cos4x)/2
and so on. In the end, you get

sin^8(x)
= 1/128 (cos8x - 8cos6x + 28 cos4x - 56cos2x + 35)