MCQ
If $\tan^{-1}(\cot\theta)=2\theta,$ then $\theta$ is equal to:
  • A
    $\frac{\pi}{3 }$
  • B
    $\frac{\pi}{4}$
  • $\frac{\pi}{6}$
  • D
    None of these.

Answer

Correct option: C.
$\frac{\pi}{6}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

Let $P=\left[\begin{array}{ccc}-30 & 20 & 56 \\ 90 & 140 & 112 \\ 120 & 60 & 14\end{array}\right]$ and $A=\left[\begin{array}{ccc}2 & 7 & \omega^{2} \\ -1 & -\omega & 1 \\ 0 & -\omega & -\omega+1\end{array}\right]$

where $\omega=\frac{-1+ i \sqrt{3}}{2},$ and $I _{3}$ be the identity matrix of order $3$. If the determinant of the matrix $\left( P ^{-1} AP - I _{3}\right)^{2}$ is $\alpha \omega^{2},$ then the value of $\alpha$ is equal to

The shortest distance between the lines $\frac{x-4}{4}=\frac{y+2}{5}=\frac{z+3}{3}$ and $\frac{x-1}{3}=\frac{y-3}{4}=\frac{z-4}{2}$ is
Points of inflexion of the curve $y = x^4 - 6x^3+ 12x^2 + 5x + 7$ are:
If $4i + 7j + 8k,\,\,\,2i + 3j + 4k\,$ and $2i + 5j + 7k$ are the position vectors of the vertices  $ A, B$  and $C$ respectively of triangle $ABC$ . The position vector of the point where the bisector of angle $A$  meets $BC$  is
Let $f : R \rightarrow R$ be given by $f(x) = x^2 - 3.$ Then, $f^{-1}$ is given by:
Let $f$ be a differentiable function in $\left(0, \frac{\pi}{2}\right)$ If $\int\limits_{\cos x}^{1} t^{2} f(t) d t=\sin ^{3} x+\cos x-1$ then $\frac{1}{\sqrt{3}} f^{\prime}\left(\frac{1}{\sqrt{3}}\right)$ is equal to
The solution of the differential equation $\frac{{dy}}{{dx}} = 1 + x + y + xy$ is
The sum of non-real roots of the polynomial equation $x^3+3 x^2+3 x+3=0$ is
The area $($in $sq.$ units$)$ bounded by the curves $\text{y}=\sqrt{\text{x}},2\text{y}-\text{x}+3=0$ and $x-$axis lying in the first quadrant is:
If $A$ and $B$ are two matrices such that $AB = B$ and $BA = A, A^2 + B^2$ is equal to: