Column-I		Column-II
A)	$\sin \left[\frac{\pi }{3}-{\sin }^{-1}\left(-\frac{1}{2}\right)\right]$	P)	$\frac{3-\sqrt{5}}{2}$
B)	$\cos \left[{\cos }^{-1}\left(-\frac{\sqrt{3}}{2}\right)+\frac{\pi }{6}\right]$	Q)	$\frac{-24}{7}$
C)	$\tan \left[\frac{1}{2}{\cos }^{-1}\frac{\sqrt{5}}{3}\right]$	R)	1
D)	$\tan \left[2{\sin }^{-1}\frac{4}{5}\right]$	S)	-1

$A)\sin \left[\frac{\pi }{3}+\frac{\pi }{6}\right]=\sin \frac{\pi }{2}=1$

$B)\cos \left[\frac{5\pi }{6}+\frac{\pi }{6}\right]=\cos \pi =-1$

$C)let\theta ={\cos }^{-1}\frac{\sqrt{5}}{3}.$
  $\tan \frac{\theta }{2}=\sqrt{\frac{1-\cos \theta }{1+\cos \theta }}$
$=\sqrt{\frac{3-\sqrt{5}}{3+\sqrt{5}}}=\frac{3-\sqrt{5}}{2}$

$D)let\theta ={\sin }^{-1}\frac{4}{5}.$ 
$\tan 2\theta =\frac{2\left({\displaystyle \frac{4}{3}}\right)}{1-{\displaystyle \frac{16}{9}}}=-\frac{24}{7}$