Binomial Theoreom and Trigonometry

[Yaaaldi]

Homework Statement

Express cos^4Θ.sinΘ in the form asinΘ+bsin3Θ+csin5Θ

Homework Equations

cosrΘ = 1/2(z^r + z^-r)
sinrΘ = 1/2i(z^r - z^-r)

The Attempt at a Solution

So far I think I have this.

32i(sinΘ)(cos^4Θ) = (z-z^-1)(z+z^-1)^4

I am unsure how to multiply and manipulate out the brackets to get what I want, which I think is something along the lines of.

p(z - z^-1) + q(z^3 - z^-3) + r(z^5 - z^-5)

Basically need to know the best way to deal with the brackets to get it in that form^
If anything is hard to understand because of my notation, let me know and ill try clarify.

thanks

 

[vela]

If you know the binomial theorem, you can use it to expand (z+1/z)^4 quickly, but multiplying everything out by hand isn't too bad either.