The value of


The value of $\sin \left(2 \sin ^{-1}(.6)\right)$ is

(a) 0.48           

(b) 0.96             

(c) 1.2           

(d) sin 1.2


$\sin \left(2 \sin ^{-1} 0.6\right)$

$=\sin \left[\sin ^{-1}\left(2 \times 0.6 \times \sqrt{1-(0.6)^{2}}\right)\right]$                $\left[2 \sin ^{-1} x=\sin ^{-1}\left(2 x \sqrt{1-x^{2}}\right)\right]$

$=\sin \left[\sin ^{-1}(2 \times 0.6 \times \sqrt{1-0.36})\right]$

$=\sin \left[\sin ^{-1}(2 \times 0.6 \times \sqrt{0.64})\right]$

$=\sin \left[\sin ^{-1}(2 \times 0.6 \times 0.8)\right]$

$=\sin \left[\sin ^{-1}(0.96)\right]$

$=0.96$                      $\left[\sin \left(\sin ^{-1} x\right)=x, \forall x \in[-1,1]\right]$

Hence, the correct answer is option (b).


Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now