91Ó°ÊÓ

Equation \(\sin x=\log x\) has how many solutions?

\(\tan ^{-1} \frac{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}}{\sqrt{1+x^{2}}+\sqrt{1-x^{2}}}=\frac{\pi}{4}\)

$$ 2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x) $$

$$ \cot ^{-1} x>2 $$

$$ \lim _{x \rightarrow 0} \frac{\sin ^{-1} x-\tan ^{-1} x}{x^{3}} $$