Skip to main content
Back to INVERSE TRIGONOMETRY

Your Progress

0 / 605 Answered
0
Correct
0
Incorrect
0%
Accuracy
JEE • MATHEMATICS • INVERSE TRIGONOMETRY

Inverse trigonometry practice · Mixed difficulty

Choose an answer to check it, or open “View answer” to study the explanation. Sign in to save progress to your account.

Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

Take a chapter quiz →
Showing 541-570 of 605 questions

Preparing practice and saved progress…

541 Medium
541 of 605
Understanding +4 | -1
tan⁡−1x+tan⁡−1y=tan⁡−1(x+y1−xy)\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1}\left(\frac{x+y}{1-x y}\right) for
View answer and explanation
Correct option: D
xy<1x y<1
Option D (xy<1xy<1) is correct because the formula for the sum of arctangents is valid only when the product of the arguments is less than 1.
542 Medium
542 of 605
Application +4 | -1
Given that sin⁡−1(sin⁡3π4)=2πk\sin ^{-1}\left(\sin \frac{3 \pi}{4}\right)=\frac{2 \pi}{\mathrm{k}}, then k={k}=
View answer and explanation
Correct option: A
8
Option A (8) is correct because by simplifying the expression using trigonometric properties, the value of k is found to be 8.
543 Medium
543 of 605
Application +4 | -1
The value of sin⁡−1[cos⁡{cos⁡−1(cos⁡x)+sin⁡−1(sin⁡x)}]\sin ^{-1}\left[\cos \left\{\cos ^{-1}(\cos x)+\sin ^{-1}(\sin x)\right\}\right]; where x∈(π2,π)x \in\left(\frac{\pi}{2}, \pi\right) is
View answer and explanation
Correct option: D
−π2\frac{-\pi}{2}
Option D (−π2\frac{-\pi}{2}) is correct because, for x∈(π2,π)x \in (\frac{\pi}{2}, \pi), sin⁡−1(sin⁡x)=π−x\sin^{-1}(\sin x) = \pi - x and cos⁡−1(cos⁡x)=x\cos^{-1}(\cos x) = x, leading to sin⁡−1(cos⁡(π))=−π2\sin^{-1}(\cos(\pi)) = \frac{-\pi}{2}.
544 Medium
544 of 605
Application +4 | -1
If (sin⁡−1x)2−(cos⁡−1x)2=a;0<x<1;a≠0{\left( {{{\sin }^{ - 1}}x} \right)^2} - {\left( {{{\cos }^{ - 1}}x} \right)^2} = a;0 < x < 1;a \ne 0 , then the value of 2x2−12{x^2} - 1 is
View answer and explanation
Correct option: B
sin⁡(2aπ)\sin \left(\frac{2 a}{\pi}\right)
Option B (sin(2a/π)) is correct because using the identity sin-1(x) + cos-1(x) = π/2, the given equation can be simplified to express cos-1(x) in terms of a, and then 2x2 - 1 can be expressed as sin(2a/π).
545 Medium
545 of 605
Application +4 | -1
For which value of x,sin⁡[cot⁡−1(x+1)]=cos⁡(tan⁡−1x)x, \sin \left[\cot ^{-1}(x+1)\right]=\cos \left(\tan ^{-1} x\right) is
View answer and explanation
Correct option: D
−12-\frac{1}{2}
Option D (−12-\frac{1}{2}) is correct because it is the solution to the equation obtained by equating the sine and cosine expressions after simplification.
546 Medium
546 of 605
Application +4 | -1
The number of positive integral solutions of the equation tan⁡−1x+cot⁡−1y=tan⁡−13\tan ^{-1} x+\cot ^{-1} y=\tan ^{-1} 3, is
View answer and explanation
Correct option: A
two
Option A (two) is correct because there are only two positive integral solutions that satisfy the given equation.
547 Easy
547 of 605
Application +4 | -1
If θ∈[4  π,  5  π]\theta \in \left[ {4\;\pi ,\;5\;\pi } \right], then cos⁡−1(cos⁡θ){\cos ^{ - 1}}\left( {\cos \theta } \right) equals
View answer and explanation
Correct option: A
−4  π+θ- 4\;\pi + \theta
Option C (4π−θ4\pi - \theta) is correct because, within the given range for θ\theta, the expression cos⁡−1(cos⁡θ){\cos ^{ - 1}}(\cos \theta ) simplifies to this value.
548 Easy
548 of 605
Application +4 | -1
If cos⁡−1p+cos⁡−11−p+cos⁡−11−q=3π4,{\cos ^{ - 1}}\sqrt p + {\cos ^{ - 1}}\sqrt {1 - p} + {\cos ^{ - 1}}\sqrt {1 - q} = \frac{{3\pi }}{4}, then the value of qq is
View answer and explanation
Correct option: D
12\frac{1}{2}
Option D (12\frac{1}{2}) is correct because solving the given equation involving inverse cosines leads to q=12q = \frac{1}{2}.
549 Easy
549 of 605
Understanding +4 | -1
sin⁡−1(2x1+x2)=2tan⁡−1x\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)=2 \tan ^{-1} x for
View answer and explanation
Correct option: C
∣x∣≤1|x| \leq 1
Option C (∣x∣≤1|x| \leq 1) is correct because the identity sin⁡−1(2x1+x2)=2tan⁡−1x\sin ^{-1}(\frac{2 x}{1+x^2})=2 \tan ^{-1} x holds true only when ∣x∣≤1|x| \leq 1.
550 Easy
550 of 605
Application +4 | -1
If cos⁡−1x+cos⁡−1y=π2  {\cos ^{ - 1}}x + {\cos ^{ - 1}}y = \frac{\pi }{2}\; and tan⁡−1x−tan⁡−1y=0,  {\tan ^{ - 1}}x - {\tan ^{ - 1}}y = 0,\; then x2+xy+y2  {x^2} + xy + {y^2}\; is equal to
View answer and explanation
Correct option: C
32\frac{3}{2}
Option C is correct because given the conditions cos⁡−1x+cos⁡−1y=π2{\cos ^{ - 1}}x + {\cos ^{ - 1}}y = \frac{\pi }{2} and tan⁡−1x−tan⁡−1y=0{\tan ^{ - 1}}x - {\tan ^{ - 1}}y = 0, it follows that x2+xy+y2=32{x^2} + xy + {y^2} = \frac{3}{2}.
551 Hard
551 of 605
Understanding +4 | -1
sin⁡−1x+sin⁡−11x+cos⁡−1x+cos⁡−11x{\sin ^{ - 1}}x + {\sin ^{ - 1}}\frac{1}{x} + {\cos ^{ - 1}}x + {\cos ^{ - 1}}\frac{1}{x} is equal to
View answer and explanation
Correct option: A
π\pi
Option A (π\pi) is correct because the sum of inverse trigonometric functions simplifies to π\pi using the properties of inverse sine and cosine.
552 Medium
552 of 605
Analyzing +4 | -1
If the sum of the series tan⁡−13+tan⁡−192+tan⁡−1334+……\tan ^{-1} 3+\tan ^{-1} \frac{9}{2}+\tan ^{-1} \frac{33}{4}+\ldots \ldots to nn terms == (2n+1)πA+Btan⁡−1(2n)\frac{(2 n+1) \pi}{A}+B \tan ^{-1}\left(2^n\right) then (A+B)(A+B) is equal to
View answer and explanation
Correct option: D
3
Option A (-√(5/3) < x < √(5/3)) is correct because solving the inequality leads to the condition x² < 5/3, which gives the specified range for x.
553 Easy
553 of 605
Application +4 | -1
If tan⁡−1k−tan⁡−13=tan⁡−1113\tan ^{-1} k-\tan ^{-1} 3=\tan ^{-1} \frac{1}{13}, then k=k=
View answer and explanation
Correct option: A
4
Option A (4) is correct because by applying the tangent subtraction formula and solving for k, the value of k is found to be 4.
554 Easy
554 of 605
Application +4 | -1
If cos⁡−1xa+cos⁡−1yb=5π12\cos ^{-1} \frac{x}{a}+\cos ^{-1} \frac{y}{b}=\frac{5 \pi}{12} and sin⁡−1xa−sin⁡−1yb=π12\sin ^{-1} \frac{x}{a}-\sin ^{-1} \frac{y}{b}=\frac{\pi}{12} then x2a2+y2b2\frac{x^2}{a^2}+\frac{y^2}{b^2} is
View answer and explanation
Correct option: D
54\frac{5}{4}
Option B (32e\frac{3}{2} \sqrt{e}) is correct because by solving the differential equation and applying the given condition, we can find y(4).
555 Medium
555 of 605
Application +4 | -1
If f(x)=2tan⁡−1x+sin⁡−1(2x1+x2),x>1f(x)=2 \tan ^{-1} x+\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right), x>1 then f(5)f(5) is equal to :
View answer and explanation
Correct option: C
π\pi
Option C (π\pi) is correct because after simplification, the function f(x)f(x) becomes a constant function equal to π\pi for x>1x>1.

Explore Other Chapters in MATHEMATICS

View All →
SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs
556 Easy
556 of 605
Application +4 | -1
If 12sin⁡−1[3sin⁡2θ5+4cos⁡2θ]=tan⁡−1x\frac{1}{2} \sin ^{-1}\left[\frac{3 \sin 2 \theta}{5+4 \cos 2 \theta}\right]=\tan ^{-1} x, then x=x=
View answer and explanation
Correct option: C
(1/3)tan⁡θ(1 / 3) \tan \theta
Option C ((1/3)tan(theta)) is correct because, by simplifying the expression inside the inverse sine function and using trigonometric substitutions, we find that x = (1/3)tan(theta).
557 Easy
557 of 605
Application +4 | -1
If 2tan⁡−1(cos⁡x)=tan⁡−1(2  cosec  x)2{\tan ^{ - 1}}\left( {\cos x} \right) = {\tan ^{ - 1}}\left( {2\;\mathrm{cosec}\;x} \right), then the value of xx is
View answer and explanation
Correct option: B
π4\frac{\pi }{4}
Option B (π4\frac{\pi}{{4}}) is correct because solving the given trigonometric equation involving inverse tangent and cosecant functions leads to x = π4\frac{\pi}{{4}}.
558 Easy
558 of 605
Application +4 | -1
If x∈[−1,0)x \in[-1,0) then cos⁡−1(2x2−1)−2sin⁡−1x\cos ^{-1}\left(2 x^2-1\right)-2 \sin ^{-1} x equals
View answer and explanation
Correct option: D
None of these
Option D (None of these) is correct because the expression simplifies to a constant value, but that value is not among the given options.
559 Easy
559 of 605
Application +4 | -1
tan⁡−1mn−tan⁡−1m−nm+n{\tan ^{ - 1}}\frac{m}{n} - {\tan ^{ - 1}}\frac{{m - n}}{{m + n}} is equal to
View answer and explanation
Correct option: A
π4\frac{\pi }{4}
Option A (π4\frac{\pi}{4}) is correct because simplifying the expression using the tangent subtraction formula leads to π4\frac{\pi}{4}.
560 Easy
560 of 605
Application +4 | -1
sin⁡(cos⁡−1(45))=\sin \left(\cos ^{-1}\left(\frac{4}{5}\right)\right)=
View answer and explanation
Correct option: C
35\frac{3}{5}
Option C (3/5) is correct because sin(cos-1(4/5)) can be simplified by considering a right triangle where cos(θ) = 4/5, which implies sin(θ) = 3/5.
561 Easy
561 of 605
Application +4 | -1
cot⁡{cos⁡−1(725)}  =\cot \left\{ {{{\cos }^{ - 1}}\left( {\frac{7}{{25}}} \right)} \right\}\; =
View answer and explanation
Correct option: D
None of these
The correct answer is D (None of these) because the value of the expression simplifies to 7/24, which is not among the given options.
562 Medium
562 of 605
Application +4 | -1
The value of cos⁡(2cos⁡−1x+sin⁡−1x)\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right) at x=15x=\frac{1}{5} is
View answer and explanation
Correct option: A
−265-\frac{2 \sqrt{6}}{5}
Option A (−265-\frac{2 \sqrt{6}}{5}) is correct because the expression simplifies using trigonometric identities and the given value of x.
563 Medium
563 of 605
Application +4 | -1
If tan⁡−1x−1x−2+tan⁡−1x+1x+2=π4\tan ^{-1} \frac{x-1}{x-2}+\tan ^{-1} \frac{x+1}{x+2}=\frac{\pi}{4}, then x=x=
View answer and explanation
Correct option: C
±12\pm \frac{1}{\sqrt{2}}
Option C (±12\pm \frac{{1}}{{\sqrt{{2}}}}) is correct because it is obtained by applying the tangent addition formula and solving the resulting quadratic equation.
564 Easy
564 of 605
Application +4 | -1
The value of cos⁡(2cos⁡−1x+sin⁡−1x)  at  x=15  \cos (2{\cos ^{ - 1}}x + {\sin ^{ - 1}}x)\;\mathrm{at}\;x = \frac{1}{5}\; is
View answer and explanation
Correct option: D
−265- \frac{{2\sqrt 6 }}{5}
Option D (−265- \frac{{2\sqrt 6 }}{5}) is correct because it involves simplifying the expression using trigonometric identities and substituting the given value of x.
565 Easy
565 of 605
Application +4 | -1
The value of tan⁡−112+tan⁡−113+tan⁡−178{\tan ^{ - 1}}\frac{1}{2} + {\tan ^{ - 1}}\frac{1}{3} + {\tan ^{ - 1}}\frac{7}{8} is
View answer and explanation
Correct option: C
tan⁡−115{\tan ^{ - 1}}15
The correct answer is C (tan⁡−115{\tan ^{ - 1}}15) because it results from applying the arctangent addition formula twice to simplify the expression.
566 Easy
566 of 605
Application +4 | -1
A continuous even periodic function ff with period 8 is such that f(0)=0,f(1)=−2,f(2)=1,f(3)=2,f(4)=3f(0)=0, f(1)=-2, f(2)=1, f(3)=2, f(4)=3 then the value of tan⁡−1(tan⁡(f(−5)+f(20)+cos⁡−1(f(−10)+f(17))))\tan ^{-1}\left(\tan \left(f(-5)+f(20)+\cos ^{-1}(f(-10)+f(17))\right)\right) is equal to:
View answer and explanation
Correct option: B
5−2π5-2 \pi
Option B (5−2π5-2 \pi) is correct because after simplification using the properties of trigonometric functions and inverse trigonometric functions, the expression evaluates to 5−2π5-2 \pi.
567 Medium
567 of 605
Application +4 | -1
Solution of the equation 2tan⁡−1(cos⁡x)=tan⁡−1(2cosec⁡x)2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x) is
View answer and explanation
Correct option: B
x=nπ+π4;n∈Zx=n \pi+\frac{\pi}{4} ; n \in \mathbb{Z}
Option B (x=nπ+π4;n∈Zx=n \pi+\frac{\pi}{4} ; n \in \mathbb{Z}) is correct because it represents the solution to the given equation after applying trigonometric identities and solving for x.
568 Medium
568 of 605
Analyzing +4 | -1
If f(x)=sin⁡−1(x−x−1x(x+1))f(x)=\sin ^{-1}\left(\frac{\sqrt{x}-\sqrt{x-1}}{\sqrt{x(x+1)}}\right) then f1(x)=f^1(x)=
View answer and explanation
Correct option: A
12(1x(x+1)−1xx−1)\frac{1}{2}\left(\frac{1}{\sqrt{x}(x+1)}-\frac{1}{x \sqrt{x-1}}\right)
Option A is correct. The derivative is found by first simplifying the function using trigonometric identities and then differentiating.
569 Easy
569 of 605
Application +4 | -1
The value of cos⁡−1(−sin⁡7π6)\cos ^{-1}\left(-\sin \frac{7 \pi}{6}\right)
View answer and explanation
Correct option: C
π3\frac{\pi}{3}
Option C (π3\frac{{\pi}}{{3}}) is correct because it correctly evaluates the sine function and then applies the inverse cosine function.
570 Easy
570 of 605
Analyzing +4 | -1
If sin⁡−1x+sin⁡−1y+sin⁡−1z=π,  then  x4+y4+z4+4x2y2z2=k(x2y2+y2z2+z2x2){\sin ^{ - 1}}x + {\sin ^{ - 1}}y + {\sin ^{ - 1}}z = \pi ,\;\mathrm{then}\;{x^4} + {y^4} + {z^4} + 4{x^2}{y^2}{z^2} = k\left( {{x^2}{y^2} + {y^2}{z^2} + {z^2}{x^2}} \right) Where kk is equal to
View answer and explanation
Correct option: B
2
Option B (2) is correct because by manipulating the given equation and using trigonometric identities, we can show that the constant k in the expression is equal to 2.
Revision notes and key takeaways

Review INVERSE TRIGONOMETRY in your textbook or class notes, then use this set to check your understanding.

Showing 541-570 of 605 questions

Continue Your Practice

📚 More Sets in This Chapter

Try different difficulty levels to master this topic

→ ENGINEERING MATHEMATICS - INVERSE TRIGONOMETRY MCQs (Easy) 365 MCQs → ENGINEERING MATHEMATICS - INVERSE TRIGONOMETRY MCQs (Hard) 19 MCQs → ENGINEERING MATHEMATICS - INVERSE TRIGONOMETRY MCQs (Medium) 221 MCQs
🎯 Next Chapters to Practice

Continue building your subject mastery

→ SEQUENCE OF SERIES 1764 MCQs → DEFINITE INTEGRATION 1443 MCQs → MATRICES 1363 MCQs → INDEFINITE INTEGRATION 1179 MCQs

Your practice

0 / 605 answered · 605 remaining · 0% accuracy

Progress is stored on this device. Sign in to save to your account.

✓ Correct · ✗ Incorrect · ○ Unanswered

Practice settings

Type at least 2 characters or jump directly:
🩺 NEET MCQs 🔬 JEE MCQs 🎯 JEE College Predictor Study guides 📊 Dashboard
🔓

Save your learning progress

Sign in with a free account to save your practice answers and quiz results, then return to them when you revise.

Continue with Free Account →