Skip to main content
Back to INVERSE TRIGONOMETRY

Your Progress

0 / 365 Answered
0
Correct
0
Incorrect
0%
Accuracy
JEE • MATHEMATICS • INVERSE TRIGONOMETRY

Inverse trigonometry practice · Easy

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 271-300 of 365 questions

Preparing practice and saved progress…

271 Easy
271 of 365
Application +4 | -1
The value of cot⁡−19+cosec−1414{\cot ^{ - 1}}9 + \mathrm{cose}{\mathrm{c}^{ - 1}}\frac{{\sqrt {41} }}{4} is
View answer and explanation
Correct option: B
π4\frac{\pi }{4}
Option B (π4\frac{\pi}{4}) is correct because by converting to arctangent and using the arctangent addition formula, the expression simplifies to tan⁡−1(1)\tan^{-1}(1).
272 Easy
272 of 365
Application +4 | -1
tan⁡−1(1/4)+tan⁡−1(2/9)\tan ^{-1}(1 / 4)+\tan ^{-1}(2 / 9) is equal to
View answer and explanation
Correct option: A
(1/2)cos⁡−1(3/5)(1 / 2) \cos ^{-1}(3 / 5)
Option A ((1/2)cos⁡−1(3/5)(1 / 2) \cos ^{-1}(3 / 5)) is correct because the sum of the two inverse tangent functions simplifies to tan⁡−1(1/2)\tan^{-1}(1/2), which is equal to (1/2)cos⁡−1(3/5)(1/2)\cos^{-1}(3/5).
273 Easy
273 of 365
Application +4 | -1
tan⁡−1(sin⁡1−1cos⁡1)\tan ^{-1}\left(\frac{\sin 1-1}{\cos 1}\right) equals
View answer and explanation
Correct option: D
12−π4\frac{1}{2}-\frac{\pi}{4}
Option D (12−π4\frac{1}{2}-\frac{\pi}{4}) is correct because using the half-angle formula and simplifying leads to this result.
274 Easy
274 of 365
Understanding +4 | -1
The value of sin⁡(tan⁡−1x+cot⁡−1x)sin⁡(sin⁡−1x+cos⁡−1x)\frac{\sin \left(\tan ^{-1} x+\cot ^{-1} x\right)}{\sin \left(\sin ^{-1} x+\cos ^{-1} x\right)} is
View answer and explanation
Correct option: A
1
The correct answer is A (1) because tan⁡−1x+cot⁡−1x=π2\tan^{-1}x + \cot^{-1}x = \frac{\pi}{2} and sin⁡−1x+cos⁡−1x=π2\sin^{-1}x + \cos^{-1}x = \frac{\pi}{2}, so the expression simplifies to sin⁡(π2)sin⁡(π2)=1\frac{\sin(\frac{\pi}{2})}{\sin(\frac{\pi}{2})} = 1.
275 Easy
275 of 365
Application +4 | -1
The principal value of sin⁡−1(sin⁡5π3)\sin ^{-1}\left(\sin \frac{5 \pi}{3}\right) is
View answer and explanation
Correct option: C
−π3-\frac{\pi}{3}
Option C (−π3-\frac{{\pi}}{{3}}) is correct because it is the principal value of the inverse sine function for the given value.
276 Easy
276 of 365
Application +4 | -1
The value of tan⁡[sin⁡−1(7/50)+cos⁡−1(1/50)+cot⁡−1(1/7)]\tan \left[\sin ^{-1}(7 / \sqrt{50})+\cos ^{-1}(1 / \sqrt{50})+\cot ^{-1}(1 / 7)\right] is equal to
View answer and explanation
Correct option: C
161/73161 / 73
Option C (161/73161 / 73) is the correct answer because it is the simplified result of applying trigonometric identities and the tangent addition formula.
277 Easy
277 of 365
Application +4 | -1
The value of cos⁡(2cos⁡−1x+sin⁡−1x)\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right) at x=16x=\frac{1}{6} :
View answer and explanation
Correct option: B
−356-\frac{\sqrt{35}}{6}
Option B (−356-\frac{\sqrt{35}}{6}) is correct because the expression simplifies to −1−x2-\sqrt{1-x^2} and substituting x=16x=\frac{1}{6} gives the result.
278 Easy
278 of 365
Application +4 | -1
If x>−13x > - \frac{1}{{\sqrt 3 }}, then tan⁡−1(3x−x31−3x2){\tan ^{ - 1}}\left( {\frac{{3x - {x^3}}}{{1 - 3{x^2}}}} \right) equals
View answer and explanation
Correct option: C
π+3tan⁡−1x\pi + 3{\tan ^{ - 1}}x
Option C (π+3tan⁡−1x\pi + 3{\tan ^{ - 1}}x) is correct because it accounts for the range of the arctangent function when x>−13x > - \frac{1}{{\sqrt 3 }} and applies the triple angle formula for tangent.
279 Easy
279 of 365
Application +4 | -1
The value of tan⁡−11+tan⁡−12+tan⁡−13{\tan ^{ - 1}}1 + {\tan ^{ - 1}}2 + {\tan ^{ - 1}}3, is
View answer and explanation
Correct option: C
π\pi
Option C (π\pi) is correct because by applying the formula tan⁡−1x+tan⁡−1y=π+tan⁡−1(x+y1−xy){\tan ^{ - 1}}x + {\tan ^{ - 1}}y = \pi + {\tan ^{ - 1}}\left( {\frac{{x + y}}{{1 - xy}}} \right) when xy>1xy > 1, the expression simplifies to π\pi.
280 Easy
280 of 365
Application +4 | -1
If 3sin⁡−12x1+x2−4cos⁡−11+x1+x2+2tan⁡−12x1−x2=π3,3{\sin ^{ - 1}}\frac{{2x}}{{1 + {x^2}}} - 4{\cos ^{ - 1}}\frac{{1 + x}}{{1 + {x^2}}} + 2{\tan ^{ - 1}}\frac{{2x}}{{1 - {x^2}}} = \frac{\pi }{3}, then value of xx is
View answer and explanation
Correct option: B
13\frac{1}{{\sqrt 3 }}
Option B (13\frac{1}{{\sqrt 3 }}) is correct because substituting x=tan⁡θx = \tan \theta and simplifying the equation leads to x=13x = \frac{1}{{\sqrt 3 }}.
281 Easy
281 of 365
Application +4 | -1
tan⁡−1(3x−x31−3x2)−tan⁡−1(2x1−x2){\tan ^{ - 1}}\left( {\frac{{3x - {x^3}}}{{1 - 3{x^2}}}} \right) - {\tan ^{ - 1}}\left( {\frac{{2x}}{{1 - {x^2}}}} \right) is equal to
View answer and explanation
Correct option: C
tan⁡−1x{\tan ^{ - 1}}x
Option C (tan⁡−1x{\tan ^{ - 1}}x) is correct because by substituting x=tan⁡θx = \tan{\theta}, the expression simplifies to 3tan⁡−1x−2tan⁡−1x3{\tan ^{ - 1}}x - 2{\tan ^{ - 1}}x, which equals tan⁡−1x{\tan ^{ - 1}}x.
282 Easy
282 of 365
Application +4 | -1
The value of tan {cos⁡−1(−27)−π2}\left\{ {{{\cos }^{ - 1}}\left( { - \frac{2}{7}} \right) - \frac{\pi }{2}} \right\} is
View answer and explanation
Correct option: A
235\frac{2}{{3\sqrt 5 }}
Option A (235\frac{2}{{3\sqrt 5 }}) is correct because it is the simplified value of the given trigonometric expression after applying trigonometric identities.
283 Easy
283 of 365
Remembering +4 | -1
The principal value of sin⁡−1(−32)\sin ^{-1}\left(\frac{-\sqrt{3}}{2}\right) is
View answer and explanation
Correct option: B
−π3-\frac{\pi}{3}
Option B (−π3-\frac{\pi}{3}) is correct because the principal value range for sin⁡−1(x)\sin^{-1}(x) is [−π2,π2][-\frac{\pi}{2}, \frac{\pi}{2}], and sin⁡(−π3)=−32\sin(-\frac{\pi}{3}) = -\frac{\sqrt{3}}{2}.
284 Easy
284 of 365
Understanding +4 | -1
If sin⁡−1x+sin⁡−1y=π2{\sin ^{ - 1}}x + {\sin ^{ - 1}}y = \frac{\pi }{2}, then cos⁡−1x+cos⁡−1y{\cos ^{ - 1}}x + {\cos ^{ - 1}}y is equal to
View answer and explanation
Correct option: A
π2\frac{\pi }{2}
Option A (π2\frac{\pi }{2}) is correct because if sin⁡−1x+sin⁡−1y=π2{\sin ^{ - 1}}x + {\sin ^{ - 1}}y = \frac{\pi }{2}, then cos⁡−1x+cos⁡−1y{\cos ^{ - 1}}x + {\cos ^{ - 1}}y can be derived using the identity sin⁡−1x+cos⁡−1x=π2{\sin ^{ - 1}}x + {\cos ^{ - 1}}x = \frac{\pi }{2}.
285 Easy
285 of 365
Application +4 | -1
The sum of the two angles cot⁡−13{\cot ^{ - 1}}3 and cosec−15\mathrm{cose}{\mathrm{c}^{ - 1}}\sqrt 5, is
View answer and explanation
Correct option: C
π4\frac{\pi }{4}
Option C (π4\frac{\pi }{4}) is correct because by converting both inverse cotangent and inverse cosecant to inverse tangent, the sum simplifies to tan⁡−1(1)\tan^{-1}(1), which equals π4\frac{\pi}{4}.

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
286 Easy
286 of 365
Application +4 | -1
The Principal value of cos⁡−1(cos⁡8)−sin⁡−1sin⁡8\cos ^{-1}(\cos 8)-\sin ^{-1} \sin 8 is
View answer and explanation
Correct option: C
16−5π16-5 \pi
Option C (16−5π16-5 \pi) is correct because it involves correctly finding the principal values of cos⁡−1(cos⁡8)\cos^{-1}(\cos 8) and sin⁡−1(sin⁡8)\sin^{-1}(\sin 8) and then subtracting them.
287 Easy
287 of 365
Application +4 | -1
θ=tan⁡−1(2tan⁡2θ)−tan⁡−1((1/3)tan⁡θ)\theta=\tan ^{-1}\left(2 \tan ^2 \theta\right)-\tan ^{-1}((1 / 3) \tan \theta) if tan⁡θ\tan \theta is equal to
View answer and explanation
Correct option: A
-2
Option A (-2) is correct because, after simplifying the equation using the tangent subtraction formula, we find that tan(theta) = -2 is a valid solution.
288 Easy
288 of 365
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 equal to
View answer and explanation
Correct option: A
−π/2-\pi / 2
Option A (−π/2-\pi / 2) is correct because the expression simplifies to sin⁡−1(cos⁡(π))=sin⁡−1(−1)=−π/2\sin^{-1}(\cos(\pi)) = \sin^{-1}(-1) = -\pi/2.
289 Easy
289 of 365
Application +4 | -1
2π−(sin⁡−145+sin⁡−1513+sin⁡−11665)2\pi - \left( {{{\sin }^{ - 1}}\frac{4}{5} + {{\sin }^{ - 1}}\frac{5}{{13}} + {{\sin }^{ - 1}}\frac{{16}}{{65}}} \right) is equal to
View answer and explanation
Correct option: C
3π2\frac{{3\pi }}{2}
Option C (3π2\frac{{3\pi }}{2}) is correct because it is the result of simplifying the given expression using trigonometric identities and inverse trigonometric functions.
290 Easy
290 of 365
Application +4 | -1
tan⁡−1xy−tan⁡−1x−yx+y  {\tan ^{ - 1}}\frac{x}{y} - {\tan ^{ - 1}}\frac{{x - y}}{{x + y}}\; is equal to

(where x<y>0)x < y > 0)
View answer and explanation
Correct option: B
π4\frac{\pi }{4}
Option B (π4\frac{\pi }{4}) is correct because by simplifying the expression using the tangent subtraction formula and the identity tan⁡−1(x)+cot⁡−1(x)=π2\tan^{-1}(x) + \cot^{-1}(x) = \frac{\pi}{2}, it simplifies to π4\frac{\pi}{4}.
291 Easy
291 of 365
Application +4 | -1
If x∈(−∞,  −1)x \in \left( { - \infty ,\; - 1} \right), then sin⁡−1(2x1+x2){\sin ^{ - 1}}\left( {\frac{{2x}}{{1 + {x^2}}}} \right) equals
View answer and explanation
Correct option: C
−π−2tan⁡−1x- \pi - 2{\tan ^{ - 1}}x
Option C (−π−2tan⁡−1x- \pi - 2{\tan ^{ - 1}}x) is correct because, within the specified range for xx, the expression simplifies to this form using trigonometric identities and considering the range of the arctangent function.
292 Easy
292 of 365
Application +4 | -1
The minimum value of 12π(cosec⁡−1[3x2+54]+sec⁡−1[3x2+14])\frac{12}{\pi}\left(\operatorname{cosec}^{-1}\left[3 x^2+\frac{5}{4}\right]+\sec ^{-1}\left[3 x^2+\frac{1}{4}\right]\right) is equal to (where [.] denotes the greatest integer function)
View answer and explanation
Correct option: A
2
Option A (2) is correct because by analyzing the range of the inverse trigonometric functions and the greatest integer function, the minimum value is found to be 2.
293 Easy
293 of 365
Application +4 | -1
If sin⁡−113+sin⁡−123=sin⁡−1x{\sin ^{ - 1}}\frac{1}{3} + {\sin ^{ - 1}}\frac{2}{3} = {\sin ^{ - 1}}x, then the value of xx is
View answer and explanation
Correct option: C
(5+42)9\frac{{\left( {\sqrt 5 + 4\sqrt 2 } \right)}}{9}
Option C ((5+42)9\frac{{\left( {\sqrt 5 + 4\sqrt 2 } \right)}}{9}) is correct because it uses the sine addition formula to find the value of x.
294 Easy
294 of 365
Application +4 | -1
cos⁡(2cos⁡−1x)+cos⁡(2sin⁡−1x)=0\cos \left(2 \cos ^{-1} x\right)+\cos \left(2 \sin ^{-1} x\right)=0 for
View answer and explanation
Correct option: D
−1≤x≤1-1 \leq x \leq 1
Option D (-1 ≤ x ≤ 1) is correct because the given equation simplifies to 0 for all x within the domain of both inverse cosine and inverse sine functions.
295 Easy
295 of 365
Application +4 | -1
If tan⁡−1x+tan⁡−1y+tan⁡−1z=π{\tan ^{ - 1}}x + {\tan ^{ - 1}}y + {\tan ^{ - 1}}z = \pi, then the value of x+y+zx + y + z is
View answer and explanation
Correct option: B
xyzxyz
Option B (xyzxyz) is correct because it is the simplified form of the given trigonometric equation after applying inverse trigonometric identities.
296 Easy
296 of 365
Application +4 | -1
If x>1x > 1 and 2tan⁡−1x−sin⁡−1(7/25)=π2 \tan ^{-1} x-\sin ^{-1}(7 / 25)=\pi then the value of xx is
View answer and explanation
Correct option: A
7
The correct answer is A (7) because using the given condition and trigonometric identities, we can solve for x.
297 Easy
297 of 365
Application +4 | -1
Value of cos⁡[2cos⁡−1(45)]\cos \left[2 \cos ^{-1}\left(\frac{4}{5}\right)\right] equals
View answer and explanation
Correct option: B
725\frac{7}{25}
Option A (12\frac{{1}}{{\sqrt{{2}}}}) is correct because it is the value obtained after simplifying the expression using trigonometric identities and the properties of inverse trigonometric functions.
298 Easy
298 of 365
Analyzing +4 | -1
∑m=1ntan⁡−1(2mm4+m2+2)  \sum \limits_{m = 1}^n {\tan ^{ - 1}}\left( {\frac{{2m}}{{{m^4} + {m^2} + 2}}} \right)\; is equal to
View answer and explanation
Correct option: A
tan⁡−1(n2+nn2+n+2){\tan ^{ - 1}}\left( {\frac{{{n^2} + n}}{{{n^2} + n + 2}}} \right)
Option A is correct because the given summation can be simplified using the arctangent subtraction formula and telescoping series, resulting in the expression for option A.
299 Easy
299 of 365
Application +4 | -1
The value of tan⁡{cos⁡−1(−27)−π2}\tan \left\{ {{{\cos }^{ - 1}}\left( { - \frac{2}{7}} \right) - \frac{\pi }{2}} \right\} is
View answer and explanation
Correct option: A
235\frac{2}{{3\sqrt 5 }}
Option A (235\frac{2}{{3\sqrt 5 }}) is correct because it is the simplified value obtained by using trigonometric identities and the definition of inverse trigonometric functions.
300 Easy
300 of 365
Application +4 | -1
Let tan⁡−1y=tan⁡−1x+tan⁡−1(2x1−x2),{\tan ^{ - 1}}y = {\tan ^{ - 1}}x + {\tan ^{ - 1}}\left( {\frac{{2x}}{{1 - {x^2}}}} \right), where ∣x∣<13.\left| x \right| < \frac{1}{{\sqrt 3 }}. Then, a value of yy is
View answer and explanation
Correct option: A
3x−x31−3x2\frac{{3x - {x^3}}}{{1 - 3{x^2}}}
Option A (3x−x31−3x2\frac{{3x - {x^3}}}{{1 - 3{x^2}}}) is correct because it is derived from the tangent addition formula and the double angle formula for tangent.
Revision notes and key takeaways

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

Showing 271-300 of 365 questions

Continue Your Practice

📚 More Sets in This Chapter

Try different difficulty levels to master this topic

→ ENGINEERING MATHEMATICS - INVERSE TRIGONOMETRY MCQs (All) 605 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 / 365 answered · 365 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 →