PreCal
posted by Hannah on .
verify the identity
sin x(1  2 cos^2 x + cos^4 x) = sin^5 x
12cos^2 x looks like 2cos^2x1 its just backwards. I am not sure where to start.

good observation
recall that cos 2A = 2cos^2 A  1 = 1  2sin^2 A
so 1  2 cos^2 x = 2sin^2 x  1
LS
=sin x(1  2 cos^2 x + cos^4 x)
= sinx(2sin^2 x  1 + (cos^2x)(cos^2x)
= sinx( 2 sin^2x  1 + (1sin^2x)(1 sin^2x))
= sinx(2sin^2x  1 + 1  2sin^2x + sin^4x)
= sinx(sin^4x)
= sin^5 x
= RS