Question Number 21223 by moadakennaf last updated on 16/Sep/17
$$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\left(\pi−\mathrm{2}{x}\right)\mathrm{tan}\:\left({x}\right) \\ $$
Answered by dioph last updated on 16/Sep/17
$$=\:\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{\pi−\mathrm{2}{x}}{\mathrm{cot}\:{x}}\:= \\ $$$$=\:\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{−\mathrm{2}}{−\mathrm{cosec}^{\mathrm{2}} \:{x}}\:= \\ $$$$=\:\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} \:{x}\:= \\ $$$$=\:\mathrm{2} \\ $$