precalc
posted by skye on .
use power reducing identities to prove the identity
sin^4x=1/8(34cos2x+cos4x)
cos^3x=(1/2cosx) (1+cos2x)
thanks :)

cos 2x = 2cos^2 x  1
so, 1/2 cos x (1+2cos^2 x  1) = cos^3 x
cos 4x = 1  2sin^2 2x
= 1  8sin^2 x cos^2 x
= 1  8sin^2 x (1  sin^2 x)
= 1  8sin^2 x + 8 sin^4 x
cos 2x = 1  2sin^2 x
4cos 2x = 4  8sin^2 x
1/8(34cos2x+cos4x)
= 1/8(3  4 + 8sin^2 x + 1  8sin^2 x + 8 sin^4 x)
= 1/8(8sin^4 x)
= sin^4 x