List of top Mathematics Questions on Properties of Inverse Trigonometric Functions

Evaluate: \[ \sec \left( \cos^{-1} \left( \frac{2024}{2025} \right) \right) \]

Let $(a, b) \subset(0,2 \pi)$ be the largest interval for which $\sin ^{-1}(\sin \theta)-\cos ^{-1}(\sin \theta)>, \theta \in(0,2 \pi)$, holds If $\alpha x^2+\beta x+\sin ^{-1}\left(x^2-6 x+10\right)+\cos ^{-1}\left(x^2-6 x+10\right)=0$ and $\alpha-\beta=b-a$, then $\alpha$ is equal to :

The value of $cos\left(\sin^{-1}\frac{\pi}{3}+\cos^{-1}\frac{\pi}{3}\right)$ is
The value of $\cot\left(\sum\limits^{19}_{n=1} \cot^{-1} \left(1+ \sum\limits^{n}_{p=1} 2p\right)\right) $ is :
In a triangle ABC if $\cos \, A + \cos \, B + \cos \, C = \frac{3}{2}$ , then the triangle is
The value of $\cos^{-1} \left(\cot\left(\frac{\pi}{2}\right)\right) + \cos^{-1} \left(\sin\left(\frac{2\pi}{3}\right)\right) $ is
The value of $\sin^{-1}\left ( \cos\, \frac { 53 \pi}{5}\right)$ is
The value of $2 \cot ^{-1} \frac{1}{2}-\cot ^{-1} \frac{4}{3}$ is
Solve $ {{\sin }^{-1}}\,2x+{{\cos }^{-1}}\,2x+2\,{{\tan }^{-1}}\,x=\pi $
The value of $\sin \left[\cot^{-1}\{{\cos(tan^{-1}\,x)\}}\right]$ is
The value of $\cos \left[ \frac{1}{2} \cos^{-1}\left(\cos\left(\sin^{-1} \frac{\sqrt{63}}{8}\right)\right)\right] $ is -
The value of $2 \,tan^{-1} (cosec \,tan^{-1} x - tan \,cot^{-1} x))$ is
The value of $ {{\cos }^{-1}}\,\left( \sin \,\frac{7\pi }{6} \right) $ is equal to
The solution of $\sin^{-1}\,x-\sin^{-1}\,2x=\pm\frac{\pi}{3}$ 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
$2 \, \tan^{-1}\left(\frac{1}{3}\right)+tan^{-1}\left(\frac{1}{4}\right)=$
If tan $\frac{\theta}{2}=\frac{1}{2}$,then the value of sin $\theta$ is
The period of the function $f\left(x\right)= cos 4x+$ tan $3x$ is
The value of $\tan^2(\sec^{-1}2)+\cot^2(cosec^{-1}3)$ is
The value of $\:sin^{-1}\left(cos\left(\frac{33\pi }{5}\right)\right)$
The formula $2\,\sin^{-1}x=\sin^{-1}(2x\sqrt{1-x^2})$ holds for
To derive the tangent formula, the following steps are given: 1. $\tan\left(A + B\right) = \frac{\frac{\sin A \cos B}{\cos A \cos B} + \frac{\cos A \sin B}{\cos A \cos B}}{\frac{\cos A \cos B}{\sin A \sin B} + \frac{\sin A \sin B}{\cos A \cos B}}$ 2. $\tan\left(A + B\right) = \frac{\sin\left(A + B\right)}{\cos\left(A + B\right)} $ 3. $\tan\left(A + B\right) = \frac{\sin A \cos B + \cos A \sin B}{\cos A \cos B - \sin A \sin B}$ 4.$ \tan\left(A + B\right) = \frac{\tan A + \tan B}{1- \tan A \tan B} $ Their correct and proper sequential form to derive the formula is:
The value of $tan^{-1}\left(\frac{3}{4}\right)+ tan^{-1}\left(\frac{1}{7}\right)$ is