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

Question

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

✓

Answer

(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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If the vectors $3\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}}$ and $2\hat{\text{i}}-\hat{\text{j}}+8\hat{\text{k}}$ are perpendicular, then $\lambda$ is equal to:

$-14$
$7$
$14$
$\frac{1}{7}$

The vector $(\cos\text{a}\cos\beta)\hat{\text{i}}+(\cos\text{a}\sin\beta)\hat{\text{j}}+(\sin\text{a})\hat{\text{k}}$is a:

Null vector
Unit vector
Constant vector
None of these

The maximum value of Z = 4x + 3y subjected to the constraints 3x + 2y ≥ 160, 5x + 2y ≥ 200, x + 2y ≥ 80, x, y ≥ 0 is:

320
300
230
none of these

If for the matrix $A, A^3 = I,$ than $A^{-1} =$

The system of equation x + y + z = 2, 3x − y + 2z = 6 and 3x + y + z = −18 has:

A unique solution.
No solution.
An infinite number of solutions.
Zero solution as the only solution.

By graphical method, the solution of linear programming problem
Maximize $Z = 3x_1 + 5x_2$
Subject to
$3x_1 + 2x_2 \leq 18$
$x_1 \leq 4$
$x_2 \leq 6$
$x1 \geq 0, x2 \geq 0,$ is:

Area bounded by the curve $\text{y}=\log\text{x}$ and the coordinate axes is:

$2$
$1$
$5$
$2\sqrt{2}$

The sides of an equilateral triangle are increasing at the rate of 2cm/ sec. The rate at which the area increases, when side is 10cm is:

If the vectors $4 \hat{i}+11 \hat{j}+m \hat{k}, 7 \hat{i}+2 \hat{j}+6 \hat{k}$ and $\hat{i}+5 \hat{j}+4 \hat{k}$ are coplanar, then $m =$

The value of $\int_0^{\pi / 2} \frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}} d x$ will be