List of top Mathematics Questions on limits of trigonometric functions asked in MHT CET

The range of the function $y = \log(\sin x)$ where $\sin x > 0$ is:
Find the value of the following expression: \[ \tan^2(\sec^{-1}4) + \cot(\csc^{-1}3) \]

Evaluate: $$ \lim_{x \to \frac{\pi}{2}} \frac{\cot x - \cos x}{(\pi - 2x)^3} $$