NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...

## Inverse Trigonometric Functions

### Mathematics

#### Previous Years Questions

More
The sum of the absolute maximum and absolute minimum values of the function $$f(x)=\tan ^{-1}(\sin x-\cos x)$$ in the in...
JEE Main 2022 (Online) 28th July Evening Shift
Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $$... JEE Main 2022 (Online) 28th July Morning Shift If$$0 ...
JEE Main 2022 (Online) 26th July Evening Shift
$$\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)$$ is equal to :...
JEE Main 2022 (Online) 26th July Morning Shift
Let $$\alpha = \tan \left( {{{5\pi } \over {16}}\sin \left( {2{{\cos }^{ - 1}}\left( {{1 \over {\sqrt 5 }}} \right)} \r... JEE Main 2022 (Online) 30th June Morning Shift Let m and M respectively be the minimum and the maximum values of$$f(x) = {\sin ^{ - 1}}2x + \sin 2x + {\cos ^{ - 1}}2x...
JEE Main 2022 (Online) 30th June Morning Shift
The set of all values of k for which $${({\tan ^{ - 1}}x)^3} + {({\cot ^{ - 1}}x)^3} = k{\pi ^3},\,x \in R$$, is the int...
JEE Main 2022 (Online) 24th June Morning Shift
Let $$x * y = {x^2} + {y^3}$$ and $$(x * 1) * 1 = x * (1 * 1)$$. Then a value of $$2{\sin ^{ - 1}}\left( {{{{x^4} + {x^2... JEE Main 2022 (Online) 24th June Evening Shift The value of$${\tan ^{ - 1}}\left( {{{\cos \left( {{{15\pi } \over 4}} \right) - 1} \over {\sin \left( {{\pi \over 4}}...
JEE Main 2022 (Online) 25th June Evening Shift
If the inverse trigonometric functions take principal values then $${\cos ^{ - 1}}\left( {{3 \over {10}}\cos \left( {{{\... JEE Main 2022 (Online) 26th June Evening Shift$${\sin ^1}\left( {\sin {{2\pi } \over 3}} \right) + {\cos ^{ - 1}}\left( {\cos {{7\pi } \over 6}} \right) + {\tan ^{ - ...
JEE Main 2022 (Online) 27th June Morning Shift
The value of $$\cot \left( {\sum\limits_{n = 1}^{50} {{{\tan }^{ - 1}}\left( {{1 \over {1 + n + {n^2}}}} \right)} } \rig... JEE Main 2022 (Online) 27th June Evening Shift$${\cos ^{ - 1}}(\cos ( - 5)) + {\sin ^{ - 1}}(\sin (6)) - {\tan ^{ - 1}}(\tan (12))$$is equal to :(The inverse trigono... JEE Main 2021 (Online) 1st September Evening Shift Let M and m respectively be the maximum and minimum values of the function f(x) = tan$$-$$1 (sin x + cos x) in$$\left[ ...
JEE Main 2021 (Online) 27th August Evening Shift
If $${({\sin ^{ - 1}}x)^2} - {({\cos ^{ - 1}}x)^2} = a$$; 0 &lt; x &lt; 1, a $$\ne$$ 0, then the value of 2x2 $$-$$ 1 i...
JEE Main 2021 (Online) 27th August Morning Shift
If $$\sum\limits_{r = 1}^{50} {{{\tan }^{ - 1}}{1 \over {2{r^2}}} = p}$$, then the value of tan p is :
JEE Main 2021 (Online) 26th August Evening Shift
Let $$f(x) = \cos \left( {2{{\tan }^{ - 1}}\sin \left( {{{\cot }^{ - 1}}\sqrt {{{1 - x} \over x}} } \right)} \right)$$, ...
JEE Main 2021 (Online) 26th August Morning Shift
The value of $$\tan \left( {2{{\tan }^{ - 1}}\left( {{3 \over 5}} \right) + {{\sin }^{ - 1}}\left( {{5 \over {13}}} \rig... JEE Main 2021 (Online) 20th July Evening Shift The number of real roots of the equation$${\tan ^{ - 1}}\sqrt {x(x + 1)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = {\pi...
JEE Main 2021 (Online) 20th July Morning Shift
The number of solutions of the equation $${\sin ^{ - 1}}\left[ {{x^2} + {1 \over 3}} \right] + {\cos ^{ - 1}}\left[ {{x^... JEE Main 2021 (Online) 17th March Evening Shift If cot$$-$$1($$\alpha$$) = cot$$-$$1 2 + cot$$-$$1 8 + cot$$-$$1 18 + cot$$-$$1 32 + ...... upto 100 terms, then$$\alph...
JEE Main 2021 (Online) 17th March Morning Shift
The sum of possible values of x for tan$$-$$1(x + 1) + cot$$-$$1$$\left( {{1 \over {x - 1}}} \right)$$ = tan$$-$$1$$\lef... JEE Main 2021 (Online) 17th March Morning Shift Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which sa... JEE Main 2021 (Online) 16th March Evening Shift If 0 &lt; a, b &lt; 1, and tan$$-$$1a + tan$$-$$1b =$${\pi \over 4}$$, then the value of$$(a + b) - \left( {{{{a^2} +...
JEE Main 2021 (Online) 26th February Evening Shift
If $${{{{\sin }^1}x} \over a} = {{{{\cos }^{ - 1}}x} \over b} = {{{{\tan }^{ - 1}}y} \over c}$$; $$0 &lt; x &lt; 1$$, th...
JEE Main 2021 (Online) 26th February Morning Shift
cosec$$\left[ {2{{\cot }^{ - 1}}(5) + {{\cos }^{ - 1}}\left( {{4 \over 5}} \right)} \right]$$ is equal to :
JEE Main 2021 (Online) 25th February Evening Shift
A possible value of $$\tan \left( {{1 \over 4}{{\sin }^{ - 1}}{{\sqrt {63} } \over 8}} \right)$$ is :
JEE Main 2021 (Online) 24th February Evening Slot
If S is the sum of the first 10 terms of the series $${\tan ^{ - 1}}\left( {{1 \over 3}} \right) + {\tan ^{ - 1}}\left(... JEE Main 2020 (Online) 5th September Morning Slot 2$$\pi $$-$$\left( {{{\sin }^{ - 1}}{4 \over 5} + {{\sin }^{ - 1}}{5 \over {13}} + {{\sin }^{ - 1}}{{16} \over {65}}} ...
JEE Main 2020 (Online) 3rd September Morning Slot
The value of $${\sin ^{ - 1}}\left( {{{12} \over {13}}} \right) - {\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$ is equal ...
JEE Main 2019 (Online) 12th April Morning Slot
If $${\cos ^{ - 1}}x - {\cos ^{ - 1}}{y \over 2} = \alpha$$,where –1 $$\le$$ x $$\le$$ 1, – 2 $$\le$$ y $$\le$$...
JEE Main 2019 (Online) 10th April Evening Slot
If $$\alpha = {\cos ^{ - 1}}\left( {{3 \over 5}} \right)$$, $$\beta = {\tan ^{ - 1}}\left( {{1 \over 3}} \right)$$ whe...
JEE Main 2019 (Online) 8th April Morning Slot
Considering only the principal values of inverse functions, the set A = { x $$\ge$$ 0: tan$$-$$1(2x) + tan$$-$$1(3x) =...
JEE Main 2019 (Online) 12th January Morning Slot
All x satisfying the inequality (cot–1 x)2– 7(cot–1 x) + 10 &gt; 0, lie in the interval :...
JEE Main 2019 (Online) 11th January Evening Slot
The value of $$\cot \left( {\sum\limits_{n = 1}^{19} {{{\cot }^{ - 1}}} \left( {1 + \sum\limits_{p = 1}^n {2p} } \right)... JEE Main 2019 (Online) 10th January Evening Slot If&nbsp;&nbsp;x = sin$$-$$1(sin10) and y = cos$$-$$1(cos10), then y$$-$$x is equal to : JEE Main 2019 (Online) 9th January Evening Slot If$${\cos ^{ - 1}}\left( {{2 \over {3x}}} \right) + {\cos ^{ - 1}}\left( {{3 \over {4x}}} \right) = {\pi \over 2}$$(x... JEE Main 2019 (Online) 9th January Morning Slot A value of x satisfying the equation sin[cot−1 (1+ x)] = cos [tan−1 x], is : JEE Main 2017 (Online) 9th April Morning Slot The value of tan-1$$\left[ {{{\sqrt {1 + {x^2}} + \sqrt {1 - {x^2}} } \over {\sqrt {1 + {x^2}} - \sqrt {1 - {x^2}} }...
JEE Main 2017 (Online) 8th April Morning Slot
Let $${\tan ^{ - 1}}y = {\tan ^{ - 1}}x + {\tan ^{ - 1}}\left( {{{2x} \over {1 - {x^2}}}} \right),$$ where $$\left| x ... JEE Main 2015 (Offline) If$$x, y, z$$are in A.P. and$${\tan ^{ - 1}}x,{\tan ^{ - 1}}y$$and$${\tan ^{ - 1}}z$$are also in A.P., then JEE Main 2013 (Offline) The value of$$cot\left( {\cos e{c^{ - 1}}{5 \over 3} + {{\tan }^{ - 1}}{2 \over 3}} \right)$$is AIEEE 2008 If sin-1$$\left( {{x \over 5}} \right)$$+ cosec-1$$\left( {{5 \over 4}} \right)$$=$${\pi \over 2}$$, then the value ... AIEEE 2007 If$${\cos ^{ - 1}}x - {\cos ^{ - 1}}{y \over 2} = \alpha ,$$then$$4{x^2} - 4xy\cos \alpha + {y^2}$$is equal to AIEEE 2005 The trigonometric equation$${\sin ^{ - 1}}x = 2{\sin ^{ - 1}}a$$has a solution for AIEEE 2003$${\cot ^{ - 1}}\left( {\sqrt {\cos \alpha } } \right) - {\tan ^{ - 1}}\left( {\sqrt {\cos \alpha } } \right) = x,$$the... AIEEE 2002 ## Numerical More For$$k \in \mathbb{R}$$, let the solutions of the equation$$\cos \left(\sin ^{-1}\left(x \cot \left(\tan ^{-1}\left(\c...
JEE Main 2022 (Online) 27th July Morning Shift
Let $$x = \sin (2{\tan ^{ - 1}}\alpha )$$ and $$y = \sin \left( {{1 \over 2}{{\tan }^{ - 1}}{4 \over 3}} \right)$$. If $... JEE Main 2022 (Online) 25th July Evening Shift$\$50\tan \left( {3{{\tan }^{ - 1}}\left( {{1 \over 2}} \right) + 2{{\cos }^{ - 1}}\left( {{1 \over {\sqrt 5 }}} \right)}...
JEE Main 2022 (Online) 29th June Morning Shift

### Joint Entrance Examination

JEE Main JEE Advanced WB JEE

### Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

NEET

Class 12