MHT CET · Maths · Inverse Trigonometric Functions
The principal value of \(\cot ^{-1}\left(\frac{-1}{\sqrt{3}}\right)\) is
- A \(\frac{2 \pi}{3}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{-\pi}{3}\)
- D \(\frac{\pi}{6}\)
Answer & Solution
Correct Answer
(A) \(\frac{2 \pi}{3}\)
Step-by-step Solution
Detailed explanation
\(\cot ^{-1}\left(\frac{-1}{\sqrt{3}}\right)=\pi-\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)=\pi-\frac{\pi}{3}=\frac{2 \pi}{3}\)
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
- With usual notations in \(\triangle \mathrm{ABC}\), if \(\angle \mathrm{B}=\frac{\pi}{2}\), and \(\tan \frac{\mathrm{A}}{2}, \tan \frac{\mathrm{C}}{2}\) are roots of equation \(\mathrm{p} x^2+\mathrm{q} x+\mathrm{r}=0\), \(\mathrm{p} \neq 0\), thenMHT CET 2025 Medium
- If A \((3,-2,2), \mathrm{B}(2, \lambda+1,5)\) are the end points of the diameter of the circle and if
the point \((5,6,-1)\) lies on the circle, then \(\lambda=\)MHT CET 2020 Medium - Let \(\bar{a}=\hat{i}+2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}\) and \(\overline{\mathrm{b}}=\hat{i}-\hat{\mathrm{j}}+\hat{\mathrm{k}}\). If \(\overline{\mathrm{c}}\) is a vector such that \(\bar{a} \cdot \overline{\mathrm{c}}=|\overline{\mathrm{c}}|\), \(|\overline{\mathrm{c}}-\bar{a}|=2 \sqrt{2}\) and the angle between \(\overline{\mathrm{a}} \times \overline{\mathrm{b}}\) and \(\overline{\mathrm{c}}\) is \(60^{\circ}\), then \(|(\bar{a} \times \overline{\mathrm{b}}) \times \overline{\mathrm{c}}|\) is equal toMHT CET 2025 Hard
- \(\int_{0}^{\pi / 2} \frac{d x}{1+\tan x}\) is equal toMHT CET 2011 Easy
- The vector equation of the line \(\frac{x+3}{2}=\frac{2 y-3}{5} ; z=-1\) isMHT CET 2020 Easy
- \(\int_{\frac{1}{2}}^2 \frac{1}{x} \operatorname{cosec}^{101}\left(x-\frac{1}{x}\right) \mathrm{d} x=\)MHT CET 2025 Medium
More PYQs from MHT CET
- What is the minimum energy required to launch a satellite of mass ‘m’ from the surface of the earth of mass ‘M’ and radius ‘R’ at an attitude 2R?MHT CET 2019 Medium
- The excess pressure inside the first soap bubble of radius ' \(\mathrm{R}_{1}\) ' is two times, that inside the second soap bubble of radius ' \(\mathrm{R}_{2}\) '. The ratio of volumes of the first bubble to that of second bubble isMHT CET 2020 Easy
- A solid sphere rolls without slipping on an inclined plane at an angle \(\theta\). The ratio of total kinetic energy to its rotational kinetic energy isMHT CET 2023 Medium
- The number of possible solutions of \(\sin \theta+\sin 4 \theta+\sin 7 \theta=0, \theta \in(0, \pi)\) areMHT CET 2023 Hard
- A parallel plate capacitor is charged and then disconnected from the charging battery. If the plates are now moved further apart by pulling them by means of insulting handles, thenMHT CET 2022 Medium
- The curve \(x^4-2 x y^2+y^2+3 x-3 y=0\) cuts the X -axis at \((0,0)\) at an angle ofMHT CET 2024 Hard