^ - 1 x a^2 - x^2 = - Vidyadip

MCQ

${\tan ^{ - 1}}\frac{x}{{\sqrt {{a^2} - {x^2}} }} = $

A
$\frac{1}{a}{\sin ^{ - 1}}\left( {\frac{x}{a}} \right)$
B
$a{\sin ^{ - 1}}\left( {\frac{x}{a}} \right)$
✓
${\sin ^{ - 1}}\left( {\frac{x}{a}} \right)$
D
${\sin ^{ - 1}}\left( {\frac{a}{x}} \right)$

✓

Answer

Correct option: C.

${\sin ^{ - 1}}\left( {\frac{x}{a}} \right)$

c
(c) ${\tan ^{ - 1}}\frac{x}{{\sqrt {{a^2} - {x^2}} }} = {\tan ^{ - 1}}\,\left( {\frac{{a\,\sin \theta }}{{a\,\cos \theta }}} \right)$ ( Putting $x = a\,\sin \theta )$

$ = {\tan ^{ - 1}}(\tan \theta ) = \theta = {\sin ^{ - 1}}\left( {\frac{x}{a}} \right)$.

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

Integration of $\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)$ with respect to $x$ :

The equation of the curve whose slope is given by $\frac{\text{dy}}{\text{dx}}=\frac{2\text{y}}{\text{x}};\text{x}>0,\text{y}>0$ and which passes through the point (1, 1) is:

$\text{x}^{2}=\text{y}$
$\text{y}^{2}=\text{x}$
$\text{x}^{2}=2\text{y}$
$\text{y}^{2}=2\text{x}$

The set of points of discontinuity of the function $f(x)$ = $\frac{{\tan \,x.{{\tan }^{ - 1}}\left( {\frac{1}{{x - 1}}} \right)}}{{x\left( {x - 3} \right)\left( {x - 5} \right)}}$ is

One ticket is drawn from a bag containing 70 tickets numbered 1 to 70 Find the probability that it is a multiple of 5 or 7:

$\frac{1}{10}$
$\frac{1}{70}$
$\frac{6}{70}$
$\frac{11}{35}$

If the system of equations, $x + 2y -3z = 1, (k + 3) z = 3, (2k + 1)x + z = 0$ is inconsistent, then the value of $k$ is :-

Let $f ^1( x )=\frac{3 x +2}{2 x +3}, x \in R -\left\{\frac{-3}{2}\right\}$ For $n \geq 2$, define $f ^{ n }( x )= f ^1 0 f ^{ n -1}( x )$. If $f ^5( x )=\frac{ ax + b }{ bx + a }, \operatorname{gcd}( a , b )=1$, then $a + b$ is equal to $............$.

If $\sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{2}$ then $\cos ^{-1} x+\cos ^{-1} y=$ _________.

Let $\omega \neq 1$ be a cube root of unity and $S$ be the set of all non-singular matrices of the form $\left[\begin{array}{lll}1 & a & b \\ \omega & 1 & c \\ \omega^2 & \omega & 1\end{array}\right]$ where each of $a, b$, and $c$ is either $\omega$ or $\omega^2$. Then the number of distinct matrices in the set $S$ is

Let $A$ and $B$ be $3 \times 3$ real matrices such that $A$ is symmetric matrix and $B$ is skew-symmetric matrix. Then the system of linear equations $\left( A ^{2} B ^{2}- B ^{2} A ^{2}\right) X = O ,$ where $X$ is a $3 \times 1$ column matrix of unknown variables and $O$ is a $3 \times 1$ null matrix, has ....... .

$\left| {\,\begin{array}{*{20}{c}}{{b^2} - ab}&{b - c}&{bc - ac}\\{ab - {a^2}}&{a - b}&{{b^2} - ab}\\{bc - ac}&{c - a}&{ab - {a^2}}\end{array}\,} \right| = $