Question

Least integral value of $x$ for which inequality ${\sin }^{-1}\left(\sin \left(\frac{2e^x+3}{e^x+1}\right)\right)>\pi -\frac{5}{2}$ holds, is

Answer 1

${\sin }^{-1}\left(\sin \left(\frac{2e^x+3}{e^x+1}\right)\right)>\pi -\frac{5}{2}\sin \left(\frac{2e^x+3}{e^x+1}\right)>\sin (\pi -\frac{5}{2})\sin \frac{2e^x+3}{e^x+1}>\sin \frac{5}{2}\frac{2e^x+3}{e^x+1}>\frac{5}{2}4e^x+6>5e^x+51>e^{x}0>x$

Least integral value $=-1$