Find the value of [2 ^ -1 (0.6) ] - Vidyadip

Question

Find the value of $\sin \left[2 \sin ^{-1}(0.6)\right]$

✓

Answer

We know that $2 \sin ^{-1} x=\sin ^{-1}\left(2 x \sqrt{1-x^2}\right)$,
if $\frac{-1}{\sqrt{2}} \leq x \leq \frac{1}{\sqrt{2}}$
$\therefore 2 \sin ^{-1}(0.6)=\sin ^{-1}(2 \times 0.6 \times \sqrt{1-0.36})$
$=\sin ^{-1}(0.96)$
$\Rightarrow \sin \left(2 \sin ^{-1}(0.6)\right)=\sin \left(\sin ^{-1}(0.96)\right)$
$=0.96 \text { }$

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 "2 Marks Questions" 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

Write the position vector of a point dividing the line segment joining points having position vectors $\hat{\text{i}}+\hat{\text{j}}-2\hat{\text{k}}$ and $2\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}}$ externally in the ratio 2 : 3.

Find the vector in the direction of vector $2\hat{\text{i}}-3\hat{\text{j}}+6\hat{\text{k}}$ which has magnitude 21 units.

$\text{Find } \frac{\text{dy}}{\text{dx}} \text{ at t} = \frac{2\pi}{3} \text{ when x 10 (t} -\sin \text{t) and y = 12 } (1 - \cos \text{t}).$

A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall?

Find the absolute maximum value and the absolute minimum value of the function: $f(x)=(x-1)^{2}+3, x \in[-3,1]$

Evaluate the following integrals:
$\int\frac{(1+\sqrt{\text{x}})^2}{\sqrt{\text{x}}}\text{dx}$

Find the value of $\tan ^{-1}\left(-\frac{1}{\sqrt{3}}\right)+\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)+\tan ^{-1}\left[\sin \left(\frac{-\pi}{2}\right)\right].$

Show that the following triads of vectors are coplanar:
$\vec{\text{a}}=\hat{\text{i}}+2\hat{\text{j}}-\hat{\text{k}},\vec{\text{b}}=3\hat{\text{i}}+2\hat{\text{j}}+7\hat{\text{k}},\vec{\text{c}}=5\hat{\text{i}}+6\hat{\text{j}}+5\hat{\text{k}}$

A card is drawn from a well-shulffled deck of 52 cards. The outcome is noted, the card is replaced and the deck reshuffled. Another card is then drawn from the deck.
What is the probability that both the cards are of the same suit?

Find the value of the determinant $\begin{vmatrix}2^2&2^3&2^4\\2^3&2^4&2^5\\2^4&2^5&2^6\end{vmatrix}$