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## Numerical

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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

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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

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