Sin (tan–1 x), | x | < 1 is equal to - Vidyadip

Question

Sin (tan^–1 x), | x | < 1 is equal to

✓

Answer

Let tan^-1 x = y, then tan y = x $\Rightarrow$ sin y = $\frac{x}{\sqrt{1+x^{2}}}$
$\therefore$ y = sin^-1 $\left(\frac{x}{\sqrt{1+x^{2}}}\right)$
$\Rightarrow$ $\tan ^{-1} x=\sin ^{-1}\left(\frac{x}{\sqrt{1+x^{2}}}\right)$
$\Rightarrow$ sin (tan^-1 x) = sin$\left(\sin ^{-1}\left(\frac{x}{\sqrt{1+x^{2}}}\right)\right)$
= $\frac{x}{\sqrt{1+x^{2}}}$

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 "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

Show that the function given by f(x) = 3x + 17 is increasing on R.

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\frac{\text{d}^2\text{y}}{\text{dx}^2}=\Big(\frac{\text{dy}}{\text{dx}}\Big)^{\frac{2}{3}}$

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\frac{\text{d}^2\text{y}}{\text{dx}^2}+5\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)-6\text{y}=\log\text{x}$

If $\sin\bigg(\sin^{-1}\frac{1}{5}+\cos^{-1}\text{x}\bigg) = 1,$then find the vatue of x.

Construct a 2 × 2 matrix, A = $[\text{a}_{\text {ij}}]$, whose elements are given by:

$\text a_{\text {ij}}=\frac{\text i}{\text j} $

Integrate the functions in Exercises:
$\text{e}^{2\text{x}+3}$

If a dice is rolled once, then find the probability o multiple of 2 .

Find the interval in function 6 - 9x - x²is increasing or decreasing.

Show that a one – one function f : {1, 2, 3} $\to$ {1, 2, 3} must be onto.

Given an example of:
A diagonal matrix which is not scalar.