Question Number 70653 by naka3546 last updated on 06/Oct/19
$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\:\left(\mathrm{sin}\:{x}\:−\:\mathrm{cos}\:{x}\right)^{\mathrm{tan}\:{x}} \:\:=\:\:... \\ $$
Commented by kaivan.ahmadi last updated on 06/Oct/19
$${lim}_{{x}\rightarrow\frac{\pi}{\mathrm{2}}} \left({sinx}−{cosx}−\mathrm{1}\right){tanx}= \\ $$$${lim}_{{x}\rightarrow\frac{\pi}{\mathrm{2}}} \left({sin}^{\mathrm{2}} {x}−{sinx}−{tanx}\right)=−\infty \\ $$$$\Rightarrow{lim}_{{x}\rightarrow\frac{\pi}{\mathrm{2}}} \left({sinx}−{cosx}\right)^{{tanx}} ={e}^{−\infty} =\mathrm{0} \\ $$
Answered by sadimuhmud 136 last updated on 06/Oct/19
