Inverse Trigonometric Functions PYQs - Last 10 Years

MHT CET / Mathematics / Trigonometry / 163 recent questions

MathematicsTrigonometry2017-2026

All Inverse Trigonometric Functions PYQs Last 5 Years Create chapter test

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.

163

PYQs on Page

Mathematics / Trigonometry

2019-2026

Year Range

Based on indexed question metadata

140

Last 5 Years

2022-2026

163

Last 10 Years

2017-2026

Recent Year Trend

2021

2022

2023

2024

2025

2026

202147 max PYQs/year2026

Question Types

163PYQs

MCQ100%

Difficulty Mix

#1 Unknown163

140 in last 5 years163 in last 10 years

Last 10 Years Inverse Trigonometric Functions Questions

Showing 50 of 163 filtered questions.

1Inverse Trigonometric Functions

If $a_1, a_2, a_3, \ldots, a_n$ are in arithmetic progression with common difference d, then $\tan\left[\tan^{-1}\left(\dfrac{d}{1 + a_1 a_2}\right) + \tan^{-1}\left(\dfrac{d}{1 + a_2 a_3}\right) + \ldots + \tan^{-1}\left(\dfrac{d}{1 + a_{n...

2Inverse Trigonometric Functions

If $2\sin^{-1}x - 3\cos^{-1}x = 4$, then $2\sin^{-1}x + 3\cos^{-1}x =$

3Inverse Trigonometric Functions

If $3\sin^{-1}\left(\dfrac{2x}{1 + x^2}\right) - 4\cos^{-1}\left(\dfrac{1 - x^2}{1 + x^2}\right) + 2\tan^{-1}\left(\dfrac{2x}{1 - x^2}\right) = \dfrac{\pi}{3}$ then $x = ?$

4Inverse Trigonometric Functions

If $\sin^{-1}\left(\tan\dfrac{\pi}{4}\right) - \sin^{-1}\left(\sqrt{\dfrac{3}{x}}\right) = \dfrac{\pi}{6}$ then $x$ is a root of the equation

5Inverse Trigonometric Functions

$\sum\limits_{k=1}^{2026} \sin^{-1}\left(\cos\dfrac{k\pi}{4}\right) =$

6Inverse Trigonometric Functions

The lengths of the shadows of a tree of height p, thrown by sun's rays at three different moments are p, 2p and 3p. The sum of the angles of elevation of the sun's rays at these three moments is equal to...

7Inverse Trigonometric Functions

The value of $\sin^{-1}\left(\sin\dfrac{5\pi}{6}\right) + \cos^{-1}\left(\cos\dfrac{7\pi}{6}\right) + \tan^{-1}\left(\tan\dfrac{2\pi}{3}\right)$ is equal to...

8Inverse Trigonometric Functions

If $\sum\limits_{n=1}^{2026}\tan^{-1}\left(\dfrac{1}{n^2+n+1}\right) = \tan^{-1}\left(1 - \dfrac{1}{x}\right)$, where $x \neq 0$, then $x = $

9Inverse Trigonometric Functions

If $0 \leq x \leq 1$ and $(\sin^{-1}x)^3 + (\cos^{-1}x)^3 = a\pi^3$ then

10Inverse Trigonometric Functions

If $y = \tan^{-1}\left(\dfrac{\log\left(\dfrac{e}{x^3}\right)}{\log ex^3}\right) + \tan^{-1}\left(\dfrac{\log(e^4x^3)}{\log\left(\dfrac{e}{x^{12}}\right)}\right)$, $x \in \left(e^{-\frac{1}{3}}, e^{\frac{1}{12}}\right)$ then $\dfrac{dy}{dx}...

11Inverse Trigonometric Functions

$\sec^2(\tan^{-1}3) - \tan^2(\sec^{-1}3) = $

12Inverse Trigonometric Functions

If $\tan^{-1}ax + \tan^{-1}3x = \dfrac{\pi}{4}$, where $3ax^2 < 1$, then value of $a$ for $x = \dfrac{1}{6}$ is $\ldots$

13Inverse Trigonometric Functions

For $x > 0$, if $\sin(\cos^{-1}x + \tan^{-1}x) - \cos(\sin^{-1}x + \tan^{-1}x) = \sin(\cot^{-1}2)$ then $x = $

14Inverse Trigonometric Functions

The value of $3\tan^{-1}\left(\dfrac{1}{2}\right) = \ldots$

15Inverse Trigonometric Functions

$\cos^{-1}\left(\cos\dfrac{4\pi}{3}\right) + \sin^{-1}\left(\sin\dfrac{4\pi}{3}\right) = \ldots$

16Inverse Trigonometric Functions

$\sin\left(3\sin^{-1}\left(\dfrac{1}{5}\right)\right) =$

17Inverse Trigonometric Functions

If $\sin^{-1}(x - 2) + \cos^{-1}(x) + \tan^{-1}(x + 2) + \cot^{-1}(x + 4) = \sec^{-1}(\sqrt{k}) - \dfrac{\pi}{2}$, then $\cos(2\,\text{cosec}^{-1}\sqrt{k - 1}) = \ldots$

18Inverse Trigonometric Functions

$\sin^{-1}\left(\dfrac{12}{13}\right) + \cos^{-1}\left(\dfrac{4}{5}\right) + \tan^{-1}\left(\dfrac{63}{16}\right) =$

19Inverse Trigonometric Functions

$\cos\left(\cos^{-1}\left(-\dfrac{1}{2}\right) + \dfrac{\pi}{3}\right) =$

20Inverse Trigonometric Functions

If $(\tan^{-1}x)^2 + (\cot^{-1}x)^2 = \dfrac{5\pi^2}{8}$, then the value of $x$ is equal to...

21Inverse Trigonometric Functions

The value of $\cot^{-1}\left[\dfrac{\sqrt{1 - \sin x} + \sqrt{1 + \sin x}}{\sqrt{1 - \sin x} - \sqrt{1 + \sin x}}\right]$, where $x \in \left(0, \dfrac{\pi}{2}\right)$ is...

22Inverse Trigonometric Functions

If $\tan^{-1}\left[\dfrac{\sqrt{5-2\sqrt{6}}}{1+\sqrt{6}}\right] = \dfrac{\pi}{3} - \tan^{-1}(k)$, then $\sec^{-1}(k) = ...$

23Inverse Trigonometric Functions

The value of $\tan^{-1}\left(\dfrac{\cos\left(\frac{19\pi}{4}\right) - 1}{\sin\left(\frac{\pi}{4}\right)}\right)$ is equal to

24Inverse Trigonometric Functions

The value of $\tan^{-1}(\sqrt{3}) + \sec^{-1}(-2) - \sin^{-1}\left(-\dfrac{1}{2}\right)$ is

25Inverse Trigonometric Functions

The value of $\dfrac{\tan^{-1}(1) + \cos^{-1}\left(\dfrac{1}{2}\right) + \sin^{-1}\left(\dfrac{1}{2}\right)}{\tan^{-1}(\sqrt{3}) - \sec^{-1}(-2)}$ is equal to

26Inverse Trigonometric Functions

Let $f(x) = (\sin^{-1} x)^2 + (\cos^{-1} x)^2$ be a real-valued function defined on its domain. Then the sum of the greatest and the least values of $f(x)$ is

27Inverse Trigonometric Functions

If $\tan^{-1}(1) + \tan^{-1}(3) + \tan^{-1}(5) + \tan^{-1}\left(\dfrac{1}{4}\right) = \pi + \tan^{-1}\left(\dfrac{\alpha}{2}\right)$, then the value of $\alpha$ is...

28Inverse Trigonometric Functions

The minimum value of $(\sin^{-1} x)^2 + (\cos^{-1} x)^2$ is............

29Inverse Trigonometric Functions

If $\cot(\cos^{-1} x) = \sec\left(\tan^{-1} \dfrac{a}{\sqrt{b^2 - a^2}}\right)$, then the value of $x$ is

30Inverse Trigonometric Functions

If $x=\tan ^{-1}\left\{\frac{\sqrt{1+t^2}-1}{t}\right\}, y=\cos ^{-1}\left\{\frac{1-t^2}{1+t^2}\right\}, \quad$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

31Inverse Trigonometric Functions

\(\cot ^{-1}\left(2 \cdot 1^2\right)+\cot ^{-1}\left(2 \cdot 2^2\right)+\cot ^{-1}\left(2 \cdot 3^2\right)+\ldots \ldots \ldots \infty=\)

32Inverse Trigonometric Functions

The value of $\tan \left[2 \tan ^{-1} \frac{1}{5}-\frac{\pi}{4}\right]$ is

33Inverse Trigonometric Functions

The number of positive integral solutions of $\tan ^{-1} x+\cos ^{-1}\left(\frac{y}{\sqrt{1+y^2}}\right)=\sin ^{-1}\left(\frac{3}{\sqrt{10}}\right)$ are

34Inverse Trigonometric Functions

If $\sin ^{-1}(4 x)+\sin ^{-1}(4 \sqrt{3} x)=-\frac{\pi}{2}$, then the value of $x$ is

35Inverse Trigonometric Functions

If $y=\tan ^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right), 0 \leqslant x<\frac{\pi}{2}$, then $y^{\prime}\left(\frac{\pi}{6}\right)=$

36Inverse Trigonometric Functions

Considering only the principal values of the inverse trigonometric functions, the value of $\tan \left(\sin ^{-1}\left(\frac{3}{5}\right)-2 \cos ^{-1}\left(\frac{2}{\sqrt{5}}\right)\right)$ is

37Inverse Trigonometric Functions

$$ \begin{array}{r}If\,\,\,\, y=\tan ^{-1}\left(\frac{1}{1+x+x^2}\right)+\tan ^{-1}\left(\frac{1}{x^2+3 x+3}\right) +\tan ^{-1}\left(\frac{1}{x^2+5 x+7}\right) \end{array} $$
then the value of $y^{\prime}(0)$ is

38Inverse Trigonometric Functions

If $\cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x$, then the value of $\sin x$ is

39Inverse Trigonometric Functions

The principal value of $\cos ^{-1}\left[\frac{1}{\sqrt{2}}\left(\cos \frac{9 \pi}{10}-\sin \frac{9 \pi}{10}\right)\right]$ is

40Inverse Trigonometric Functions

If $y=\tan ^{-1}\left(\frac{4 x}{1+5 x^2}\right)+\cot ^{-1}\left(\frac{3-2 x}{2+3 x}\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

41Inverse Trigonometric Functions

If $\tan ^{-1}(x+1)+\tan ^{-1} x+\tan ^{-1}(x-1)=\tan ^{-1} 3$, then for $x<0$ the value of $500 x^4+270 x^2+997=$

42Inverse Trigonometric Functions

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

43Inverse Trigonometric Functions

The value of $\tan ^2\left(\sec ^{-1} 4\right)+\cot ^2\left(\operatorname{cosec}^{-1} 3\right)$ is

44Inverse Trigonometric Functions

If $\left(\cos ^{-1} x\right)^2-\left(\sin ^{-1} x\right)^2>0$, then

45Inverse Trigonometric Functions

If $0 \leqslant \cos ^{-1} x \leqslant \pi$ and $\frac{-\pi}{2} \leqslant \sin ^{-1} x \leqslant \frac{\pi}{2}$, then at $x=\frac{1}{5}$ the value of $\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right)$ is

46Inverse Trigonometric Functions

If $3 \sin ^{-1}\left(\frac{2 x}{1+x^2}\right)-4 \cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)+2 \tan ^{-1}\left(\frac{2 x}{1-x^2}\right)=\frac{\pi}{3}$ then the value of $x=$

47Inverse Trigonometric Functions

\(\cot ^{-1}\left(2 \cos \left(2 \operatorname{cosec}^{-1}(\sqrt{2})\right)\right)=\ldots\)

48Inverse Trigonometric Functions

If $y=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)+\sec ^{-1}\left(\frac{1+x^2}{1-x^2}\right)$ then the value of $\frac{d y}{d x}$ at $x=\sqrt{3}$ is

49Inverse Trigonometric Functions

The derivative of $\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$ w.r.t. $\tan ^{-1}\left(\frac{2 x \sqrt{1-x^2}}{1-2 x^2}\right)$ at $x=0$ is

50Inverse Trigonometric Functions

The number of solutions of $\tan ^{-1}\left(x+\frac{2}{x}\right)-\tan ^{-1}\left(\frac{4}{x}\right)-\tan ^{-1}\left(x-\frac{2}{x}\right)=0$ are