If ^ -1 ( )=2 , then is equal to - Vidyadip

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.

$\frac{\pi}{6}$

$\text { (c) }: \tan ^{-1}(\cot \theta)=2 \theta$
$\Rightarrow \cot \theta=\tan 2 \theta$
$\Rightarrow \cot \theta=\cot \left(\frac{\pi}{2}-2 \theta\right)$
$\Rightarrow \theta=\frac{\pi}{2}-2 \theta$
$\Rightarrow 3 \theta=\frac{\pi}{2}$
$\Rightarrow \theta=\frac{\pi}{6}$

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

Explore more

More "M.C.Q (1 Marks)" from Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$\int_{}^{} {5\sin xdx = } $

The area of the region bounded by the ellipse $\frac{\text{x}^2}{25}+\frac{\text{y}^2}{16}=1$ is:

Let $A$ be $2$$ \times $$2$ matrix

Statement $-1 :$ $adj\left( {adj\;A} \right) = A$

Statement $-2 :$ $\left| {adj\;A} \right| = \left| A \right|$

Determinant $\left|\begin{array}{cc}1 & \log _b a \\ \log _a b & 1\end{array}\right|=$

Let $X_1$ and $X_2$ are optimal solutions of a $\ce{LPP},$ then:

If $f(x)=\left\{\begin{array}{ccc}\frac{1}{|x|} & ; & |x| \geq 1 \\ a x^{2}+b & ; & |x|<1\end{array}\right.$ is differentiable at every point of the domain, then the values of $a$ and $b$ are respectively

If $f: R \rightarrow R, f(x)=2 x+1$, then the value of $f^{-1}(5)$ is

${\tan ^{ - 1}}\frac{{a - b}}{{1 + ab}} + {\tan ^{ - 1}}\frac{{b - c}}{{1 + bc}} = $

A force of magnitude $6 $ acts along the vector $(9,\,6,\, - 2)$ and passes through a point $A$ $(4, -1, -7).$ The moment of the force about the point $O (1, -3, 2)$ is

$\int_{}^{} {\frac{{\sin 2x}}{{{{\sin }^4}x + {{\cos }^4}x}}dx = } $