List of top Mathematics Questions on Properties of Inverse Trigonometric Functions asked in KEAM

$\sec(\cos^{-1}(\frac{2024}{2025}))$ is equal to ________.
Evaluate: \[ \sec \left( \cos^{-1} \left( \frac{2024}{2025} \right) \right) \]
If tan $\frac{\theta}{2}=\frac{1}{2}$,then the value of sin $\theta$ is
If $x=5+2$ sec $\theta$ and $y=5+2\, \tan \, \theta ,$ then $\left(x-5\right)^{2}-\left(y-5\right)^{2}$ is equal to
If sin $\left(\theta-\phi\right) = n \, sin (\theta - \phi),n \ne1,$ then the value of $\frac{\tan\theta}{\tan\phi}$ is equal to
$ \tan\left(\frac{\pi}{4} +\frac{\theta}{2}\right) + \tan\left(\frac{\pi}{4} - \frac{\theta}{2}\right)$ is equal to
$2 \, \tan^{-1}\left(\frac{1}{3}\right)+tan^{-1}\left(\frac{1}{4}\right)=$
The period of the function $f\left(x\right)= cos 4x+$ tan $3x$ is