Simplifying sin(A)sin^3(B) for Integration?

[T-7]

Hi,

Just a quick trig. question:

What's the best way to expand sin(A)sin^3(B) into a suitable form for integration? (A and B are both functions of x here. As it happens, A = j*pi*x/a and B = pi*x/a)

I have written an expression in terms of elements such as cos(A-B), cos(A+B) etc., but it's a little long, and I'm inclined to think there might be a shorter way of doing it -- something obvious that I'm not thinking of (?).

My final result: 3/8*cos(A-B) - 3/8*cos(A+B) + 1/8*cos(A+3B) - 1/8*cos(A-3B)

(I used identities for sinAsinB, and for cosAcosB several times, and for cos 2B).

Cheers!

 

[Kurdt]

You could get rid of the sin³ term using a power reduction formula.

http://en.wikipedia.org/wiki/List_of_trigonometric_identities