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Question 5

5. By considering ei⁢θ=cos⁡θ+i⁢sin⁡θe^{i\theta}=\cos\theta+i\sin\theta or otherwise, show that

cos5⁡θ=116⁢cos⁡5⁢θ+516⁢cos⁡3⁢θ+58⁢cos⁡θ,\cos^{5}\theta={{1}\over{16}}\cos 5\theta+{{5}\over{16}}\cos 3\theta+{{5}\over% {8}}\cos\theta,

and deduce the indefinite integral

∫cos5⁡θ⁢d⁢θ.\int\cos^{5}\theta\,d\theta.

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