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Question Number 63763 by aliesam last updated on 08/Jul/19

Commented by Prithwish sen last updated on 08/Jul/19

$$\frac{2}{1+\cos \left(2\mathrm{x}\right)+\mathrm{i}\sin \left(2\mathrm{x}\right)}=\frac{2\{1+\cos \left(2\mathrm{x}\right)-\mathrm{isin}\left(2\mathrm{x}\right)\}}{1+2\cos \left(2\mathrm{x}\right)+{\cos }^2\left(2\mathrm{x}\right)+{\sin }^2\left(2\mathrm{x}\right)}$$$$=\frac{1+\cos \left(2\mathrm{x}\right)-\mathrm{isin}\left(2\mathrm{x}\right)}{1+\cos \left(2\mathrm{x}\right)}=1-\mathrm{i}\frac{2\mathrm{sinx}.\mathrm{cosx}}{{2\cos }^2\mathrm{x}}$$$$=1-\mathrm{itanx}\mathrm{Hence}\mathrm{proved}.$$

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