Considering only the principal values, if ( ^ - 1 x) = [ ^ - 1 ( … - Vidyadip

MCQ

Considering only the principal values, if $\tan ({\cos ^{ - 1}}x)$ $ = \sin \left[ {{{\cot }^{ - 1}}\left( {\frac{1}{2}} \right)} \right]$, then $x$ is equal to

A
$\frac{1}{{\sqrt 5 }}$
B
$\frac{2}{{\sqrt 5 }}$
C
$\frac{3}{{\sqrt 5 }}$
✓
$\frac{{\sqrt 5 }}{3}$

✓

Answer

Correct option: D.

$\frac{{\sqrt 5 }}{3}$

d
(d) Put ${\cot ^{ - 1}}\,\left( {\frac{1}{2}} \right) = \theta \,\, \Rightarrow \cot \theta = \frac{1}{2}$
$\therefore$ $\sin \theta = \frac{2}{{\sqrt 5 }}.$ Put ${\cos ^{ - 1}}x = \phi $, $\therefore$ $x = \cos \phi $
Also, $\tan \phi = \frac{2}{{\sqrt 5 }},\,\,\,\,\,\therefore \,x = \cos \phi = \frac{{\sqrt 5 }}{3}$.

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 2. inverse trigonometric function→2. inverse trigonometric function — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Using determinants, find the area (in sq. units) of triangle with vertices $(-3,5),(3,-6)$ and $(7,2)$.

If $A=\left[a_{i j}\right]$ is a skew-symmetric matrix of order $n$, then

The value of $\int_1^2 {\log x\,dx} $ is

Choose the correct answer from the given four options.
The sine of the angle between the straight line $\frac{\text{x}-2}{3}=\frac{\text{y}-2}{3}=\frac{\text{z}-2}{3}$ and the plane $2\text{x}-2\text{y}+\text{z}=5$ is:

$\frac{10}{6\sqrt{5}}$
$\frac{4}{5\sqrt{2}}$
$\frac{2\sqrt{3}}{5}$
$\frac{\sqrt{2}}{10}$

If $f(n) = \tan ^{{ - 1 }} \left( {\frac{e-1}{e^{-n}+e^{n+1}}} \right)$$\forall n\, \in \,N$ , then $\sum\limits_{n = 1}^\infty {f\left( n \right)} $ is equal to

Let $\overrightarrow{P R}=3 \hat{i}+\hat{j}-2 \hat{k}$ and $\overrightarrow{S Q}=\hat{i}-3 \hat{j}-4 \hat{k}$ determine diagonals of a parallelogram $P Q R S$ and $\overrightarrow{P T}=\hat{i}+2 \hat{j}+3 \hat{k}$ be another vector. Then the volume of the parallelepiped determined by the vectors $\overrightarrow{ PT }, \overrightarrow{ PQ }$ and $\overrightarrow{ PS }$ is

Let $f(x)$ and $g(x)$ be two functions given by $f\left( x \right) = \frac{{2\sin \pi x}}{x}$ and $g\left( x \right) = f\left( {1 - x} \right) + f\left( x \right).$ If $g\left( x \right) = kf(\frac{x}{2})f\left( {\frac{{1 - x}}{2}} \right)$,then the value of $k$ is

The differential equation for the family of curves ${x^2} + {y^2} - 2ay = 0,$ where $a$ is an arbitrary constant, is

The solution set of $f ' (x) > g ' (x),$ where $ f(x)$$ = \frac{1}{2} (5^{2x + 1}) $ $\,\, \& \,\, g(x) = 5^x + 4x (ln \,\, 5)$ is :

Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+5\, \hat{\mathrm{j}}+\alpha\, \hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+3 \,\hat{\mathrm{j}}+\beta\, \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}=-\hat{\mathrm{i}}+2\, \hat{\mathrm{j}}-3 \,\hat{\mathrm{k}}$ be three vectors such that, $|\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}|=5 \sqrt{3}$ and $\overrightarrow{\mathrm{a}}$ is perpendicular to $\overrightarrow{\mathrm{b}}$. Then the greatest amongst the values of $|\vec{a}|^{2}$ is .... .