Goodmarks

Mathematics · JEE

Inverse trigonometrical functions and their properties Revision for JEE

14+ syllabus-aligned questions available

Quick answer

Revise Inverse trigonometrical functions and their properties by covering every subtopic once, drilling formulas, then solving 14+ timed MCQs with full solutions.

Use this Inverse trigonometrical functions and their properties revision checklist before mocks and the final exam. Reinforce concepts with 14+ syllabus-aligned MCQs on Goodmarks.

Revision checklist

  1. 1.Core idea: Inverse trigonometrical functions and their properties
  2. 2.Relates to other subtopics in Trigonometry
  3. 3.Trigonometric identities
  4. 4.Inverse trig functions and properties
  5. 5.Master Inverse trigonometrical functions and their properties definitions and standard results
  6. 6.Solve 20 timed MCQs for Inverse trigonometrical functions and their properties

Syllabus context

Part of Trigonometry in JEE Main Mathematics.

Free sample questions

Attempt 8 free MCQs for Inverse trigonometrical functions and their properties. Unlock 6+ more with Pro.

Unlock full bank
Q1MathsUnit 14: Trigonometry
Assertion Consider f(x)=sin⁡−1(sec⁡(tan⁡−1x)+\boldsymbol{f}(\boldsymbol{x})=\sin ^{-1}\left(\sec \left(\tan ^{-1} \boldsymbol{x}\right)+\right. cos⁡−1(cosec⁡(cot⁡−1x)\cos ^{-1}\left(\operatorname{cosec}\left(\cot ^{-1} x\right)\right. Statement-1: Domain of f(x)f(x) is a singleton. Reason Statement-2: Range of the function f(x)\boldsymbol{f}(\boldsymbol{x}) is a singleton.
Q2MathsUnit 14: Trigonometry
The number of real solutions of the equation tan⁡−1x(x+1)+\tan ^{-1} \sqrt{x(x+1)}+ sin⁡−1x2+x+1=π2\sin ^{-1} \sqrt{x^{2}+x+1}=\frac{\pi}{2} is
Q3MathsUnit 14: Trigonometry
If value of x\mathbf{x} which satisfy equation (cot⁡−1x)2−3(cot⁡−1x)+2>0\left(\cot ^{-1} x\right)^{2}-3\left(\cot ^{-1} x\right)+2>0 is x<x< cot⁡a\cot a or x>cot⁡bx>\cot b Find the value of a+ba+b
Q4MathsUnit 14: Trigonometry
Statement I: The equation (sin⁡−1x)3+(cos⁡−1x)3−aπ3=0\left(\sin ^{-1} x\right)^{3}+\left(\cos ^{-1} x\right)^{3}-a \pi^{3}=0 has solution for all a⩾132a \geqslant \frac{1}{32} Statement II : For any xϵR,sin−1x+\boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R}, \boldsymbol{s} \boldsymbol{i n}^{-1} \boldsymbol{x}+ cos⁡−1x=π2\cos ^{-1} x=\frac{\pi}{2} and 0≤(sin⁡−1x−π4)2≤0 \leq\left(\sin ^{-1} x-\frac{\pi}{4}\right)^{2} \leq 9π216\frac{9 \pi^{2}}{16}
Q5MathsUnit 14: Trigonometry
Assertion (A)(A) If 0<x<π20<x<\frac{\pi}{2} then sin⁡−1(cos⁡x)+cos⁡−1(sin⁡x)=π−2x\sin ^{-1}(\cos x)+\cos ^{-1}(\sin x)=\pi-2 x Reason (R)cos⁡−1x=π2−sin⁡−1x∀x∈(\mathrm{R}) \cos ^{-1} x=\frac{\pi}{2}-\sin ^{-1} x \forall x \in [0,1][\mathbf{0}, \mathbf{1}]
Q6MathsUnit 14: Trigonometry
Assertion fi=12nsin⁡−1xi=nπ∀nϵNf_{i=1}^{2 n} \sin ^{-1} x_{i}=n \pi \forall n \epsilon N then ∑i=12nxi=\sum_{i=1}^{2 n} x_{i}= ∑i=12nxi2=∑i=12nxin=2n\sum_{i=1}^{2 n} x_{i}^{2}=\sum_{i=1}^{2 n} x_{i}^{n}=2 n Reason −π2≤sin⁡−1x≤π2∀xϵ[−1,1]-\frac{\pi}{2} \leq \sin ^{-1} x \leq \frac{\pi}{2} \forall x \epsilon[-1,1]
Q7MathsUnit 14: Trigonometry
Find the value of sin⁡−1x+sin⁡−11x+\sin ^{-1} x+\sin ^{-1} \frac{1}{x}+ cos⁡−1x+cos⁡−11x\cos ^{-1} x+\cos ^{-1} \frac{1}{x}
Q8MathsUnit 14: Trigonometry
If [sin⁡−1cos⁡−1sin⁡−1tan⁡−1θ]=1,\left[\sin ^{-1} \cos ^{-1} \sin ^{-1} \tan ^{-1} \theta\right]=1, where [.] denotes the greatest integer function, the θ\theta lies in the interval

Want unlimited Inverse trigonometrical functions and their properties practice?

Pro unlocks the full question bank, topic filters, and attempt history.

Get started freeView Pro plans

Popular questions in Inverse trigonometrical functions and their properties

Frequently asked questions

How should I revise Inverse trigonometrical functions and their properties before JEE?

Follow the checklist on this page, revise formulas daily, and attempt mixed MCQs every 2–3 days.

Related topics