Question

The value of sin (2sin^-1(.6)) is
(a) 0.48 (b) 0.96 (c) 1.2 (d) sin 1.2

Answer 1

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

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

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

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

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

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

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

Hence, the correct answer is option (b).