Question Number 116177 by Khalmohmmad last updated on 01/Oct/20
Commented by Dwaipayan Shikari last updated on 01/Oct/20
$$\mathrm{tan}\left(\mathrm{x}−\frac{\pi}{\mathrm{2}}\right)\mathrm{tan}\left(\mathrm{x}+\frac{\pi}{\mathrm{2}}\right)=\mathrm{1} \\ $$$$\mathrm{tan}\left(\mathrm{x}−\frac{\pi}{\mathrm{2}}\right)=\mathrm{cot}\left(\mathrm{x}+\frac{\pi}{\mathrm{2}}\right) \\ $$$$\mathrm{tan}\left(\mathrm{x}−\frac{\pi}{\mathrm{2}}\right)=\mathrm{tan}\left(−\mathrm{x}\right) \\ $$$$\mathrm{x}−\frac{\pi}{\mathrm{2}}=\mathrm{k}\pi+\left(−\mathrm{x}\right) \\ $$$$\mathrm{2x}=\mathrm{k}\pi+\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{x}=\frac{\mathrm{k}}{\mathrm{2}}\pi+\frac{\pi}{\mathrm{4}}\:\:\:\:\:\:\left(\mathrm{k}\in\mathbb{Z}\right) \\ $$