^ -1 1-x^2 x equal to : - Vidyadip

MCQ

$\cot ^{-1} \frac{\sqrt{1-x^2}}{x}$ equal to :

A
$\sin ^{-1}\left(\frac{1}{x}\right)$
✓
$\operatorname{cosec}^{-1}\left(\frac{1}{x}\right)$
C
$\tan ^{-1}\left(\frac{1}{x}\right)$
D
None of these

✓

Answer

Correct option: B.

$\operatorname{cosec}^{-1}\left(\frac{1}{x}\right)$

(B)
$\cot ^{-1} \frac{\sqrt{1-x^2}}{x}$
taking $x=\sin \theta$
$\Rightarrow \quad \cot ^{-1} \frac{\sqrt{1-\sin ^2 \theta}}{\sin \theta}=\cot ^{-1} \frac{\cos \theta}{\sin \theta}$
$\Rightarrow \quad \cot ^{-1}(\cot \theta)=\theta=\sin ^{-1} x=\operatorname{cosec}^{-1}\left(\frac{1}{x}\right)$
Hence correct option is (B).

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

If $ 5$ is one root of the equation $\left| {\,\begin{array}{*{20}{c}}x&3&7\\2&x&{ - 2}\\7&8&x\end{array}\,} \right| = 0$, then other two roots of the equation are

A particle moves in a straight line so that its velocity at any point is given by ${v^2} = a + bx$, where $a,b \ne 0$ are constants. The acceleration is

The value of $\int\frac{\text{d}(\text{x}^2+1)}{\sqrt{\text{x}^2+2}}$ is:

Out of $11$ consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in $A.P.$ with positive common difference, is

The function $f(x)=1-x^3-x^5$ is decreasing for

If the solution curve, of the differential equation $\frac{d y}{d x}=\frac{x+y-2}{x-y}$ passing through the point $(2,1)$ is $\tan ^{-1}\left(\frac{y-1}{x-1}\right)-\frac{1}{\beta} \log _e\left(\alpha+\left(\frac{y-1}{x-1}\right)^2\right)=\log _e|x-1|$, then $5 \beta+\alpha$ is equal to

Function $\text{f}(\text{x})=\cos\text{x}-2\lambda\text{x}$ is monotonic decreasing when :

If $\tan ^{-1} \frac{x-1}{x-2}+\tan ^{-1} \frac{x+1}{x+2}=\frac{\pi}{4},$ then find the value of $\mathrm{x}$

If $y = {\sin ^{ - 1}}(x\sqrt {1 - x} + \sqrt x \sqrt {1 - {x^2})} , $ then ${{dy} \over {dx}} = $

Vikas printing company takes fee of Rs. 28 to print a oversized poster and Rs. 7 for each colour of ink used. Raaj printing company does the same work and charges poster for Rs. 34 and Rs. 5.50 for each colour of ink used. If z is the colours of ink used, find the values of z such that Vikas printing company would charge more to print a poster than Raaj printing company.