Download App

Inverse Trigonometric Functions — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSInverse Trigonometric Functions1 Mark
Question
$\sin \left(\tan ^{-1} x\right)$, where $|x|<1$, is equal to
✓

Answer

We have, $\sin \left(\tan ^{-1} x\right)$
Let $\tan ^{-1} x=\theta \Rightarrow x=\tan \theta \Rightarrow \sin \theta=\frac{x}{\sqrt{x^2+1}}$
$\therefore \quad \sin \left(\tan ^{-1} x\right)=\sin \theta=\frac{x}{\sqrt{x^2+1}}$

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

The value of $\frac{0.76\times0.76\times0.76+0.24\times0.24\times0.24}{0.76\times0.76-0.76\times0.24+ 0.24+0.24}$ is:
→
If $A=\left[\begin{array}{cc}0 & 2 \\ 3 & -4\end{array}\right]$ and $k A=\left[\begin{array}{cc}0 & 3 a \\ 2 b & 24\end{array}\right]$, then the values of $k, a$ and $b$ respectively are
→
$\cos ^{-1}\left(\frac{1}{2}\right)+2 \sin ^{-1}\left(\frac{1}{2}\right)+4 \tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)$ is equal to
→
If $A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]$, then find $A^{-1}$.
→
If $\text{P(A)}=\frac{2}{5},\text{P(B)}=\frac{3}{10}$ and $\text{P}(\text{A}\cap\text{B})=\frac{1}{5},$ then, $\text{P}(\overline{\text{A}}|\overline{\text{B}}) \text{ P}(\overline{\text{B}}|\overline{\text{A}})$ is equal to
  1. $\frac{5}{6}$
  2. $\frac{5}{7}$
  3. $\frac{25}{42}$
  4. $1$
→
The points (k − 1, k + 2), (k, k + 1), (k + 1, k) are collinear for:
  1. any value of k
  2. k = −21​ only
  3. no value of k
  4. integral values of k only
→
The probability distribution of a random variable $X$ is:
$X$ $ 0$ $1$ $2$ $3$ $4$
$P(X)$ $ 0.1$ $ k$ $ 2k$ $ k$ $0.1$
where $k$ is some unknown constant.
The probability that the random variable $X$ takes the value $2$ is:
→
Direction cosines of ray from P(1, -2, 4) to Q(-1, 1, -2) are:
  1. -2, 3, -6
  2. 2, -3, 6
  3. 2, 3, 6
  4. $\frac{-2}{7},\frac{3}{7},\frac{-6}{7}$
→
The direction cosines of the ray P(1, -2, 4) and Q(-1, 1, -2) are:
  1. $\big(-2, -3, -6\big)$
  2. $\big(2, -3, -6\big)$
  3. $\Big(\frac{2}{7},\frac{3}{7},\frac{6}{7}\Big)$
  4. $\Big(-\frac{2}{7},\frac{3}{7},-\frac{6}{7}\Big)$
→
Integrating factor of the differential equation $\cos\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}\sin\text{x}=1$ is: 
  1. $\cos\text{x}$
  2. $\tan\text{x}$
  3. $\sec\text{x}$
  4. $\sin\text{x}$ 
→