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JEE • MATHEMATICS • INVERSE TRIGONOMETRY

Inverse trigonometry practice · Mixed difficulty

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601 Medium
601 of 605
Application +4 | -1
The value of cos⁡(12cos⁡−118)\cos \left(\frac{1}{2} \cos ^{-1} \frac{1}{8}\right) is equal to
View answer and explanation
Correct option: A
3/43 / 4
Option A (3/4) is correct because using the half-angle formula for cosine, we can find the value of the expression.
602 Easy
602 of 605
Application +4 | -1
The value of sec⁡[tan⁡−1(b+ab−a)−tan⁡−1(ab)]\sec \left[ {{{\tan }^{ - 1}}\left( {\frac{{b + a}}{{b - a}}} \right) - {{\tan }^{ - 1}}\left( {\frac{a}{b}} \right)} \right] is
View answer and explanation
Correct option: B
2\sqrt 2
Option B (2\sqrt 2) is correct because simplifying the expression using the tangent subtraction formula and then finding the secant of the result gives this value.
603 Medium
603 of 605
Analyzing +4 | -1
Let SS be the set of all solutions of the equation
cos⁡−1(2x)−2cos⁡−1(1−x2)=π,x∈[−12,12]. \cos ^{-1}(2 x)-2 \cos ^{-1}\left(\sqrt{1-x^{2}}\right)=\pi, x \in\left[-\frac{1}{2}, \frac{1}{2}\right] \text {. }
Then ∑x∈S2sin⁡−1(x2−1)\sum\limits_{{x \in S}} 2 \sin ^{-1}\left(x^{2}-1\right) is equal to
View answer and explanation
Correct option: A
−2π3\frac{-2 \pi}{3}
Option A (−2π3\frac{{-2 \pi}}{{3}}) is correct because solving the equation and substituting the result into the expression yields this value.
604 Easy
604 of 605
Analyzing +4 | -1
If x∈(−π2,π2),x \in \left( { - \frac{\pi }{2},\frac{\pi }{2}} \right), then the value of

tan⁡−1(tan⁡x4)+tan⁡−1(3sin⁡2x5+3cos⁡2x){\tan ^{ - 1}}\left( {\frac{{\tan x}}{4}} \right) + {\tan ^{ - 1}}\left( {\frac{{3\sin 2x}}{{5 + 3\cos 2x}}} \right) is
View answer and explanation
Correct option: D
xx
Option D (xx) is correct because the expression simplifies to tan⁡−1(tan⁡x){\tan ^{ - 1}}(\tan x), which equals xx within the given interval.
605 Medium
605 of 605
Application +4 | -1
cos⁡−1(12(cos⁡7π5−sin⁡2π5))\cos ^{-1}\left(\frac{1}{\sqrt{2}}\left(\cos \frac{7 \pi}{5}-\sin \frac{2 \pi}{5}\right)\right) is equal to
View answer and explanation
Correct option: D
17π20\frac{17 \pi}{20}
Option D (17π20\frac{17 \pi}{20}) is correct because it is obtained by simplifying the expression inside the inverse cosine function using trigonometric identities and then evaluating the inverse cosine.
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