Question Number 156058 by VIDDD last updated on 07/Oct/21
$$\:\:{cos}\frac{\pi}{\mathrm{8}}=...?\:\:{with}\:{solution}\:{plz} \\ $$
Answered by cortano last updated on 07/Oct/21
$$\:\mathrm{cos}\:\frac{\pi}{\mathrm{4}}=\mathrm{2cos}\:^{\mathrm{2}} \frac{\pi}{\mathrm{8}}−\mathrm{1} \\ $$$$\:\mathrm{cos}\:\frac{\pi}{\mathrm{8}}=\sqrt{\frac{\mathrm{1}+\mathrm{cos}\:\frac{\pi}{\mathrm{4}}}{\mathrm{2}}} \\ $$
Commented by puissant last updated on 08/Oct/21
$$\Rightarrow\:{cos}\frac{\pi}{\mathrm{8}}=\sqrt{\frac{\mathrm{1}+\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}}{\mathrm{2}}}\:\Rightarrow\:{cos}\frac{\pi}{\mathrm{8}}=\frac{\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}}{\mathrm{2}}.. \\ $$