Sample QuestionsInverse Trigonometric Functions questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The domain of function $\cos ^{-1}(2 x-3)$ is :
- A
$[-1,1]$
- B
$(1,2)$
- C
- ✓
$[1,2]$
Answer: D.
View full solution →The principal value of $\tan ^{-1}\left(\tan \frac{9 \pi}{8}\right)$ :
- ✓
$\frac{\pi}{8}$
- B
$\frac{3 \pi}{8}$
- C
$\frac{-\pi}{8}$
- D
$\frac{-3 \pi}{8}$
Answer: A.
View full solution →The principal value of $\cos ^{-1}\left(\frac{1}{2}\right)+\sin ^{-1}\left(\frac{-1}{\sqrt{2}}\right)$
- ✓
$\frac{\pi}{12}$
- B
$\pi$
- C
$\frac{\pi}{3}$
- D
$\frac{\pi}{6}$
Answer: A.
View full solution →The domain of function $f(x)=\sin ^{-1} x+\cos x$ is-
- ✓
$[-1,1]$
- B
$[-1, \pi+1]$
- C
$[-\infty, \infty]$
- D
$\phi$
Answer: A.
View full solution →Domain of $f(x)=\sin ^{-1}\left(-x^2\right)$ is :
- A
$[0,1]$
- B
$(0,1)$
- ✓
$[-1,1]$
- D
$\phi$
Answer: C.
View full solution →Find the value of $3 \cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)+\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)$
View full solution →Find the principal value of $\cos ^{-1}\left(\frac{1}{\sqrt{2}}\right)$
View full solution →Find the value of expression $2 sec ^{-1} 2+\sin ^{-1}\left(\frac{1}{2}\right)$
View full solution →Find the domain of $f(x)=\cos ^{-1}\left(x^2-4\right)$.
View full solution →If $\sin ^{-1} x=\frac{\pi}{3}$ then write the value of $\cos ^{-1} x$
View full solution →Find the value of $\tan \left(\frac{1}{2} \cos ^{-1} \frac{2}{\sqrt{5}}\right)$.
View full solution →Find the value of $\sin ^{-1}\left(\cos \frac{3 \pi}{5}\right)$.
View full solution →Find the value of $\sec ^{-1}(-2)-\sin ^{-1}\left(\frac{1}{2}\right)$.
View full solution →Prove that $\tan ^{-1} \frac{2}{3}=\frac{1}{2} \tan ^{-1} \frac{12}{5}$
View full solution →If $\sin ^{-1} x=\frac{1}{2}$ then write the value of $\sin ^{-1}\left\{2 x \sqrt{1-x^2}\right\}$.
View full solution →Solve : $\tan ^{-1}(1)+\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right)$
View full solution →If $\cos ^{-1} \alpha+\cos ^{-1} \beta+\cos ^{-1} \gamma=3 \pi$ then find the value of $\alpha(\beta+\gamma)+\beta(\gamma+\alpha)+\gamma(\alpha+\beta)$
View full solution →Write in the simplest form $\cos ^{-1}\left(\frac{3}{5} \cos x+\frac{4}{5} \sin x\right)$, where $\frac{\pi}{2} \leq x \leq \frac{3 \pi}{4}$.
View full solution →Prove that :$\tan ^{-1}\left\{\frac{\sqrt{1+\cos x}+\sqrt{1-\cos x}}{\sqrt{1+\cos x}-\sqrt{1-\cos x}}\right\}=\frac{\pi}{4}+\frac{x}{2}, 0 < x <\frac{\pi}{2}$
View full solution →If $x, y, z \in[-1,1]$ such that $\sin ^{-1} x+\sin ^{-1} y+$ $\sin ^{-1} z=\frac{-3 \pi}{2}$ then find the value of $x^2+y^2+z^2$.
View full solution →Prove that $\frac{1}{2} \tan ^{-1} x=\cos ^{-1}\left\{\frac{1+\sqrt{1+x^2}}{2 \sqrt{1+x^2}}\right\}^{\frac{1}{2}}$
View full solution →Prove that $\cos \left[\tan ^{-1}\left\{\sin \left(\cot ^{-1} x\right)\right\}\right]=\sqrt{\frac{1+x^2}{2+x^2}}$
View full solution →The range of principal value branch of $y=\sec ^{-1} x$ is _________
View full solution →The principal value of $\cos ^{-1}\left(-\frac{1}{2}\right)$ is _________
View full solution →$\tan ^{-1}\left(\tan \frac{2 \pi}{3}\right)=$ __________
View full solution →The value of $\sin ^{-1}\left(\cos \frac{33 \pi}{5}\right)$ is. ________
View full solution →The value of $\tan \left[\cos ^{-1}\left\{\sin \left(\cot ^{-1} 1\right)\right\}\right]$ is. ________
View full solution →Prove that $\tan ^{-1}\left(\frac{63}{16}\right)=\sin ^{-1}\left(\frac{5}{13}\right)+\cos ^{-1}\left(\frac{3}{5}\right)$
View full solution →Prove that $ \begin{array}{l} \tan ^{-1}\left[\frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{1+x}-\sqrt{1-x}}\right]=\frac{\pi}{4}+\frac{1}{2} \cos ^{-1} x ,0 < x < 1 \end{array} $
View full solution →Prove that $\tan \left(\frac{\pi}{4}+\frac{1}{2} \cos ^{-1} \frac{x}{y}\right)+\tan \left(\frac{\pi}{4}-\frac{1}{2} \cos ^{-1} \frac{x}{y}\right)=\frac{2 y}{x}$
View full solution →$\cos ^{-1} \frac{1-a^2}{1+a^2}+\cos ^{-1} \frac{1-b^2}{1+b^2}=2 \tan ^{-1} x$
View full solution →