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Question Number 31549 by de best last updated on 10/Mar/18

$$witoutusingcalculator,simpify$$$$cos22.5°$$

Answered by $@ty@m last updated on 10/Mar/18

$$\cos 2x=2\cos {}^{2}x-1$$$$\Rightarrow \cos x=\sqrt{\frac{1+\cos 2x}{2}}$$$$\therefore \cos 22.5^o=\sqrt{\frac{1+\cos {45}^o}{2}}$$$$=\sqrt{\frac{1+\frac{1}{\sqrt{2}}}{2}}=\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$$

Commented by MJS last updated on 10/Mar/18

$$=\frac{\sqrt{2+\sqrt{2}}}{2}$$

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