I have to verify this identity algebraically:
sin x (1 - 2 cos^2 x + cos^4 x) = sin^5 x
So I have to make the left side equal the right,
My work so far:
sin x (sin^2 x cos^2 x + 4 coos x)
sin x (sin^2 x [1 - sin^2 x] + 4 cos^4 x)
sin x ([sin^2 x - sin^4 x] + 4 cos^4 x)
sin x ([sin^2 x + cos^4 x + 1] + 4 cos^4 x)
sin x (sin^2 x + 5 cos^4 x + 1)
Now I am stuck. Am I correct so far? If I am, what do I do next?
Any help is appreciated.