Inverse Trigonometric Functions · Mathematics · JEE Advanced

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MCQ (Single Correct Answer)

JEE Advanced 2023 Paper 2 Online
For any $y \in \mathbb{R}$, let $\cot ^{-1}(y) \in(0, \pi)$ and $\tan ^{-1}(y) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$. Then the sum of all the...
JEE Advanced 2014 Paper 2 Offline
Match List $$I$$ with List $$II$$ and select the correct answer using the code given below the lists: $$\,\,\,\,$$ $$\,\,\,\,$$ $$\,\,\,\,$$ List-$$I$...
JEE Advanced 2013 Paper 2 Offline
Match List $$I$$ with List $$II$$ and select the correct answer using the code given below the lists: List $$I$$ $$P.$$$$\,\,\,\,\,$$ $${\left( {{1 ...
JEE Advanced 2013 Paper 1 Offline
The value of $$\cot \left( {\sum\limits_{n = 1}^{23} {{{\cot }^{ - 1}}} \left( {1 + \sum\limits_{k = 1}^n {2k} } \right)} \right)$$ is
IIT-JEE 2008 Paper 1 Offline
If $$0 < x < 1$$, then $$\sqrt {1 + {x^2}} {\left[ {{{\left\{ {x\cos \left( {{{\cot }^{ - 1}}x} \right) + \sin \left( {{{\cot }^{ - 1}}x} \righ...
IIT-JEE 2004 Screening
The value of $$x$$ for which $$sin\left( {{{\cot }^{ - 1}}\left( {1 + x} \right)} \right) = \cos \left( {{{\tan }^{ - 1}}\,x} \right)$$ is
IIT-JEE 2001 Screening
If $${\sin ^{ - 1}}\left( {x - {{{x^2}} \over 2} + {{{x^3}} \over 4} - ....} \right)$$ $$$ + {\cos ^{ - 1}}\left( {{x^2} - {{{x^4}} \over 2} + {{{x^6...
IIT-JEE 1999
The number of real solutions of $${\tan ^{ - 1}}\,\,\sqrt {x\left( {x + 1} \right)} + {\sin ^{ - 1}}\,\,\sqrt {{x^2} + x + 1} = \pi /2$$ is
IIT-JEE 1994
If we consider only the principle values of the inverse trigonometric functions then the value of $$\tan \left( {{{\cos }^{ - 1}}{1 \over {5\sqrt 2 }...
IIT-JEE 1986
The principal value of $${\sin ^{ - 1}}\left( {\sin {{2\pi } \over 3}} \right)$$ is
IIT-JEE 1983
The value of $$\tan \left[ {{{\cos }^{ - 1}}\left( {{4 \over 5}} \right) + {{\tan }^{ - 1}}\left( {{2 \over 3}} \right)} \right]$$ is

Numerical

JEE Advanced 2023 Paper 1 Online
Let $\tan ^{-1}(x) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, for $x \in \mathbb{R}$. Then the number of real solutions of the equation $\sqrt{1+...
JEE Advanced 2022 Paper 1 Online
Considering only the principal values of the inverse trigonometric functions, the value of $$ \frac{3}{2} \cos ^{-1} \sqrt{\frac{2}{2+\pi^{2}}}+\frac...
JEE Advanced 2019 Paper 2 Offline
The value of $${\sec ^{ - 1}}\left( \matrix{ {1 \over 4}\sum\limits_{k = 0}^{10} {\sec \left( {{{7\pi } \over {12}} + {{k\pi } \over 2}} \right)} ...
JEE Advanced 2018 Paper 1 Offline
The number of real solutions of the equation $$\eqalign{ & {\sin ^{ - 1}}\left( {\sum\limits_{i = 1}^\infty {} {x^{i + 1}} - x\sum\limits_{i = ...
JEE Advanced 2014 Paper 1 Offline
Let f : [0, 4$$\pi$$] $$\to$$ [0, $$\pi$$] be defined by f(x) = cos$$-$$1 (cos x). The number of points x $$\in$$ [0, 4$$\pi$$] satisfying the equatio...

MCQ (More than One Correct Answer)

JEE Advanced 2021 Paper 1 Online
For any positive integer n, let Sn : (0, $$\infty$$) $$\to$$ R be defined by $${S_n}(x) = \sum\nolimits_{k = 1}^n {{{\cot }^{ - 1}}\left( {{{1 + k(k +...
JEE Advanced 2018 Paper 2 Offline
For any positive integer n, define $${f_n}:(0,\infty ) \to R$$ as$${f_n} = \sum\limits_{j = 1}^n {{{\tan }^{ - 1}}} \left( {{1 \over {1 + (x + j)(x + ...
JEE Advanced 2015 Paper 2 Offline
If $$\alpha $$ $$ = 3{\sin ^{ - 1}}\left( {{6 \over {11}}} \right)$$ and $$\beta = 3{\cos ^{ - 1}}\left( {{4 \over 9}} \right),$$ where the inverse t...

Subjective

IIT-JEE 2007
Let $$(x, y)$$ be such that $${\sin ^{ - 1}}\left( {ax} \right) + {\cos ^{ - 1}}\left( y \right) + {\cos ^{ - 1}}\left( {bxy} \right) = {\pi \over 2}...
IIT-JEE 2006
Match the following Column $$I$$ (A) $$\sum\limits_{i = 1}^\infty {{{\tan }^{ - 1}}\left( {{1 \over {2{i^2}}}} \right) = t,} $$ then tan $$t=$$ (B) ...
IIT-JEE 2002
Prove that $$\cos \,ta{n^{ - 1}}\sin \,{\cot ^{ - 1}}x = \sqrt {{{{x^2} + 1} \over {{x^2} + 2}}} $$.
IIT-JEE 1983
Find all the solution of $$4$$ $${\cos ^2}x\sin x - 2{\sin ^2}x = 3\sin x$$
IIT-JEE 1981
Find the value of : $$\cos \left( {2{{\cos }^{ - 1}}x + {{\sin }^{ - 1}}x} \right)$$ at $$x = {1 \over 5}$$, where $$0 \le {\cos ^{ - 1}}x \le \pi $$...

Fill in the Blanks

IIT-JEE 1989
The greater of the two angles $$A = 2{\tan ^{ - 1}}\left( {2\sqrt 2 - 1} \right)$$ and $$B = 3{\sin ^{ - 1}}\left( {1/3} \right) + {\sin ^{ - 1}}\lef...
IIT-JEE 1984
The numerical value of $$\tan \left\{ {2{{\tan }^{ - 1}}\left( {{1 \over 5}} \right) - {\pi \over 4}} \right\}$$ is equal to __________
IIT-JEE 1981
Let $$a, b, c$$ be positive real numbers Let $$\theta = {\tan ^{ - 1}}\sqrt {{{a\left( {a + b + c} \right)} \over {bc}}} + {\tan ^{ - 1}}\sqrt {{{b...
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