JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
\(\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)+\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)+\tan ^{-1}\left(\tan \frac{3 \pi}{4}\right) \quad\) is equal to
- A \(\frac{31 \pi}{12}\)
- B \(\frac{17 \pi}{12}\)
- C \(\frac{11 \pi}{12}\)
- D \(-\frac{3 \pi}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{11 \pi}{12}\)
Step-by-step Solution
Detailed explanation
\(\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)+\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)+\tan ^{-1} \tan \left(\frac{3 \pi}{4}\right)\) \(\sin ^{-1} \sin \left(\frac{2 \pi}{3}\right)=\pi-\frac{2 \pi}{3}=\frac{\pi}{3}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The number of relations, defined on the set {a, b, c, d}, which are both reflexive and symmetric, is equal to:JEE Mains 2026 Hard
- If \(\mathrm{y}=\mathrm{y}(\mathrm{x})\) is the solution of the differential equation, \(\mathrm{e}^{\mathrm{y}}\left(\frac{\mathrm{dy}}{\mathrm{dx}}-1\right)=\mathrm{e}^{\mathrm{x}}\) such that \(\mathrm{y}(0)=0,\) then \(\mathrm{y}(1)\) is equal toJEE Mains 2020 Hard
- Let \(y=y_{1}(x)\) and \(y=y_{2}(x)\) be two distinct solutions of the differential equation \(\frac{d y}{d x}=x+y\), with \(y _{1}(0)=0\) and \(y _{2}(0)=1\) respectively. Then, the number of points of intersection of \(y=y_{1}(x)\) and \(y=y_{2}(x)\) is.JEE Mains 2022 Hard
- The locus of the mid-points of the perpendiculars drawn from points on the line, \(\mathrm{x}=2 \mathrm{y}\) to the line \(\mathrm{x}=\mathrm{y}\) isJEE Mains 2020 Hard
- If the matrices \(A=\left[\begin{array}{ccc}{1} & {1} & {2} \\ {1} & {3} & {4} \\ {1} & {-1} & {3}\end{array}\right], B=\operatorname{adj} A\) and \(\mathrm{C}=3 \mathrm{A},\) then \(\frac{|\mathrm{adjB}|}{|\mathrm{C}|}\) is equal toJEE Mains 2020 Hard
- Let \(E _{1}, E _{2}, E _{3}\) be three mutually exclusive events such that \(P \left( E _{1}\right)=\frac{2+3 p }{6}, P \left( E _{2}\right)=\frac{2- p }{8}\) and \(P \left( E _{3}\right)\) \(=\frac{1- p }{2}\). If the maximum and minimum values of \(p\) are \(p _{1}\) and \(p _{2}\), then \(\left( p _{1}+ p _{2}\right)\) is equal to.JEE Mains 2022 Hard
More PYQs from JEE Mains
- If the area of the region \(\left\{( x , y ):\left| x ^2-2\right| \leq y \leq x \right\}\) is \(A\), then \(6 A +16 \sqrt{2}\) is equal to \(...........\).JEE Mains 2023 Hard
- If the shortest distance between the lines \(\frac{x-\lambda}{-2}=\frac{y-2}{1}=\frac{z-1}{1}\) and \(\frac{x-\sqrt{3}}{1}=\frac{y-1}{-2}=\frac{z-2}{1}\) is \(1 ,\) then the sum of all possible values of \(\lambda\) is :JEE Mains 2024 Hard
- A line is a common tangent to the circle \((x-3)^{2}+y^{2}=9\) and the parabola \(y^{2}=4 x.\) If the two points of contact \(( a , b )\) and \(( c , d )\) are distinct and lie in the first quadrant, then \(2(a+c)\) is equal to ........ .JEE Mains 2021 Hard
- For \(\mathrm{x} \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\), if \(y(x)=\int \frac{\operatorname{cosec} x+\sin x}{\operatorname{cosec} x \sec x+\tan x \sin ^2 x} d x\) and \(\lim _{x \rightarrow\left(\frac{\pi}{2}\right)^{-}} y(x)=0\) then \(y\left(\frac{\pi}{4}\right)\) is equal toJEE Mains 2024 Hard
- The set of all values of \(k\) for which \(\left(\tan ^{-1} x \right)^{3}+\left(\cot ^{-1} x \right)^{3}= k \pi^{3}, x \in R\), is the intervalJEE Mains 2022 Hard
- If \(A\) is a \(3×3\) non-singular matrix such that \(AA’=A’A \) and \( B=A^{-1}A’\) then \(BB’ \) equalsJEE Mains 2014 Medium