(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

cosrΘ = 1/2(z^r + z^-r)

sinrΘ = 1/2i(z^r - z^-r)

3. 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

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# Binomial Theoreom and Trigonometry

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