Inverse Trigonometric Functions

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Practice 163 MHT CET Mathematics questions from Inverse Trigonometric Functions. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Inverse Trigonometric Functions Questions

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1Inverse Trigonometric Functions

The numerical value of $\tan \left(2 \tan ^{-1}\left(\frac{1}{5}\right)+\frac{\pi}{4}\right)$

2Inverse Trigonometric Functions

The value of $\tan ^{-1}\left(\tan \frac{7 \pi}{6}\right)$ is

3Inverse Trigonometric Functions

If $\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=\pi$ and $x^2+y^2+z^2+k x y z=1$, then k is

4Inverse Trigonometric Functions

If $\tan ^{-1}(x+2)+\tan ^{-1}(x-2)-\tan ^{-1}\left(\frac{1}{2}\right)=0$, then one value of $x$ is

5Inverse Trigonometric Functions

Derivative of $\tan ^{-1} \sqrt{\frac{1-x}{1+x}}$ w.r.t. $\cos ^{-1}\left(4 x^3-3 x\right)$ is

6Inverse Trigonometric Functions

If $x, y, z$ are in Arithmetic Progression and $\tan ^{-1} x, \tan ^{-1} y, \tan ^{-1} z$ are also in Arithmetic progression, where $x, z>0$ and $x z<1, y<1$, then

7Inverse Trigonometric Functions

The value of $\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right)$ at $x=\frac{1}{5}$ is

8Inverse Trigonometric Functions

If $y=\sin ^2\left(\cot ^{-1} \sqrt{\frac{1+x}{1-x}}\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ has the value

9Inverse Trigonometric Functions

$\tan \left(\cos ^{-1} \frac{1}{\sqrt{2}}+\tan ^{-1} \frac{1}{2}\right)=$

10Inverse Trigonometric Functions

If \(\cos ^{-1} x-\cos ^{-1} \frac{y}{3}=\alpha\), where \(-1 \leq x \leq 1, -3 \leq y \leq 3, x \leq \frac{y}{3}\), then for all \(x, y\) \(9 x^2-6 x y \cos \alpha+y^2\) is equal to

11Inverse Trigonometric Functions

The value of \(\cot \left(\sum_\limits{n=1}^{23} \cot ^{-1}\left(1+\sum_\limits{k=1}^n 2 k\right)\right)\) is

12Inverse Trigonometric Functions

If \(\sin ^{-1} x+\cos ^{-1} y=\frac{3 \pi}{10}\), then the value of \(\cos ^{-1} x+\sin ^{-1} y\) is

13Inverse Trigonometric Functions

The value of \(\tan ^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right), |x| < \frac{1}{2}, x \neq 0\)

14Inverse Trigonometric Functions

If \(\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi\), then the value of \(x^{2025}+x^{2026}+x^{2027}\) is

15Inverse Trigonometric Functions

Given \(0 \leq x \leq \frac{1}{2}\), then the value of \(\tan \left(\sin ^{-1}\left(\frac{x}{\sqrt{2}}+\frac{\sqrt{1-x^2}}{\sqrt{2}}\right)-\sin ^{-1} x\right)\) is

16Inverse Trigonometric Functions

The value of \(\tan ^{-1}\left(\frac{1}{8}\right)+\tan ^{-1}\left(\frac{1}{2}\right)+\tan ^{-1}\left(\frac{1}{5}\right)\) is

17Inverse Trigonometric Functions

If \(\cos ^{-1} x-\cos ^{-1} \frac{y}{3}=\alpha\), where \(-1 \leq x \leq 1$, $-3 \leq y \leq 3, x \leq \frac{y}{3}\), then for all \(x, y, 9 x^2-6 x y \cos \alpha+y^2\) is equal to

18Inverse Trigonometric Functions

If \(\sum_\limits{r=1}^{50} \tan ^{-1} \frac{1}{2 r^2}=p\) then \(\tan p\) is

19Inverse Trigonometric Functions

\(x, y, z\) are in G.P. and \(\tan ^{-1} x, \tan ^{-1} y, \tan ^{-1} z\) are in A.P., then

20Inverse Trigonometric Functions

The principal value of \(\sin ^{-1}(\sin (3 \pi / 4))\) is

21Inverse Trigonometric Functions

If \(\left(\tan ^{-1} x\right)^2+\left(\cot ^{-1} x\right)^2=\frac{5 \pi^2}{8}\), then the value of \(x\) is

22Inverse Trigonometric Functions

The value of \(\tan \left(\sin ^{-1}\left(\frac{3}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right)\) is

23Inverse Trigonometric Functions

The value of \(\sin \left(\cot ^{-1} x\right)\) is

24Inverse Trigonometric Functions

If \(x=\operatorname{cosec}\left(\tan ^{-1}\left(\cos \left(\cot ^{-1}\left(\sec \left(\sin ^{-1} a\right)\right)\right)\right)\right), \mathrm{a} \in[0,1]\)

25Inverse Trigonometric Functions

If \(\tan ^{-1}\left(\frac{1-x}{1+x}\right)=\frac{1}{2} \tan ^{-1} x\), then \(x\) is

26Inverse Trigonometric Functions

The value of \(x\), for which \(\sin \left(\cot ^{-1}(x)\right)=\cos \left(\tan ^{-1}(1+x)\right)\), is

27Inverse Trigonometric Functions

\(\text { If } y=\sqrt{\frac{1-\sin ^{-1}(x)}{1+\sin ^{-1}(x)}} \text {, then } \frac{\mathrm{d} y}{\mathrm{~d} x} \text { at } x=0 \text { and } y=1 \text { is }\)

28Inverse Trigonometric Functions

The value of \(2 \tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{7}\)

29Inverse Trigonometric Functions

\(\text { The value of } \sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right) \text { is }\)

30Inverse Trigonometric Functions

If \(\alpha=3 \sin ^{-1} \frac{6}{11}\) and \(\beta=3 \cos ^{-1}\left(\frac{4}{9}\right)\), where the inverse trigonometric functions take only the principal values, then the correct option is

31Inverse Trigonometric Functions

\(\pi+\left(\sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{16}{65}\right)\) is equal to

32Inverse Trigonometric Functions

If \(\cos ^{-1} \sqrt{\mathrm{p}}+\cos ^{-1} \sqrt{1-\mathrm{p}}+\cos ^{-1} \sqrt{1-\mathrm{q}}=\frac{3 \pi}{4}\), then \(\mathrm{q}\) is

33Inverse Trigonometric Functions

The solution of the equation \(\tan ^{-1}(1+x)+\tan ^{-1}(1-x)=\frac{\pi}{2}\) is

34Inverse Trigonometric Functions

Considering only the principal values of an inverse function, the set
\(\mathrm{A}=\left\{x \geq 0 / \tan ^{-1} x+\tan ^{-1} 6 x=\frac{\pi}{4}\right\}\)

35Inverse Trigonometric Functions

If \(\tan ^{-1} a+\tan ^{-1} b+\tan ^{-1} c=\pi\), then which of the following statement is true?

36Inverse Trigonometric Functions

The value of \(\tan ^{-1}(1)+\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right)\) is

37Inverse Trigonometric Functions

The domain of the function \(\mathrm{f}(x)=\sin ^{-1}\left(\frac{|x|+5}{x^2+1}\right)\) is \((-\infty,-a] \cup[a, \infty)\). Then a is equal to

38Inverse Trigonometric Functions

If \(\tan ^{-1}\left(\frac{1-x}{1+x}\right)=\frac{1}{2} \tan ^{-1} x\), then \(x\) has the value

39Inverse Trigonometric Functions

The value of \(\sin \left(2 \sin ^{-1} 0.8\right)\) is equal to

40Inverse Trigonometric Functions

The principal value of \(\sin ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)\) is

41Inverse Trigonometric Functions

If \(y=\tan ^{-1}\left[\frac{\log \left(\frac{e}{x^2}\right)}{\log \left(e x^2\right)}\right]+\tan ^{-1}\left[\frac{3+2 \log x}{1-6 \log x}\right]\), then \(\frac{d^2 y}{d x^2}=\)

42Inverse Trigonometric Functions

The value of \(\sin ^{-1}\left(\frac{-1}{2}\right)+\sin ^{-1}\left(\frac{-\sqrt{3}}{2}\right)\) is,

43Inverse Trigonometric Functions

The value of \(\tan ^{-1} 2+\tan ^{-1} 3\) is

44Inverse Trigonometric Functions

\(\tan \left(\cos ^{-1}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right)=\)

45Inverse Trigonometric Functions

If \(\tan ^{-1}\left[\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right]=\alpha\), then the value of \(\sin 2 \alpha\) is

46Inverse Trigonometric Functions

If \(\tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\frac{\pi}{4}\), where \(x>0\), then \(x=\)

47Inverse Trigonometric Functions

\(y=\tan ^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right), 0 \leq x < \frac{\pi}{2}\), then \(\frac{d y}{d x}\) at \(x=\frac{\pi}{6}\) is

48Inverse Trigonometric Functions

\(\tan ^{-1}\left(\tan \frac{5 \pi}{6}\right)+\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)=\)

49Inverse Trigonometric Functions

If \(2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x)\), then the value of \(x\) is

50Inverse Trigonometric Functions

\(\tan ^{-1}\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)=\frac{\pi}{4}\), then the values of \(x\) are

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