Question

Use the power-reducing identities:

4 sin x cos^3 x + 4 sin^3 x cos x

Answer 1

Factor out 4 sin cos

Answer 2

??

Answer 3

4 sin cos ( cos^2 + sin^2)

Answer 4

I got that far, but would cos^2 + sin^2 then equal 1?

Answer 5

It would and 4 sin cos is equal to something as well...

Answer 6

2sin 2x? And if this is correct, can you explain why?

Answer 7

Well, because sin 2x is 2 sin x cos x (double angle formula)

Answer 8

Oh ok, gotcha. The problem is that my book doesn't actually give you the double angle formula, but rather goes a round-about way of explaining it.

Answer 9

Very confusing.

Answer 10

Yes, you should learn them, very useful.
Most things are here:
http://en.wikipedia.org/wiki/List_of_trigonometric_identities