Sin 3A

[bnielson]

This one is from Math for the Million too. I got the answer right, but the answer key gives a final step that doesn't make sense to me.

Given Sin 3A I can derive:

3 Sin A Cos^2 A - Sin^3 A

The answer book goes on to claim that is equivalent to:
3 Sin A - 4 Sin^3 A.

I can't figure out that last transformation.

Does anyone see how that is possible?

 

[bnielson]

Here is a related one:

Given Cos 3A I can derive:

Cos^3A - 3 Cos A * Sin^2 A.

But the answer key claims this can be changed into:
4 Cos^3 A - 3 Cos A

how?

 

[mmm4444bot]

3 Sin A Cos^2 A - Sin^3 A

The answer book goes on to claim that [this] is equivalent to:

3 Sin A - 4 Sin^3 A

One way to get from the former to the latter is to first factor out sin(A), and then rewrite the cos(A)^2 factor in terms of sin(A)^2.