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Question Number 169295 by thfchristopher last updated on 28/Apr/22

$$\mathrm{Prove}\mathrm{without}\mathrm{using}\mathrm{Mathematical}$$$$\mathrm{Induction}\mathrm{that}:$$$${\cos }^{n}x=\frac{1}{2^{n-1}}\underset{k=0}{\sum ^{(n-1)/2}}{C}_k^n\cos (n-2k)x$$$$\mathrm{where}x\mathrm{is}\mathrm{any}\mathrm{real}\mathrm{number}\mathrm{and}n\mathrm{is}\mathrm{any}$$$$\mathrm{positive}\mathrm{odd}\mathrm{integer}.$$

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