Question 482089
use a half angle identity to find the exact value of the expression 
sin 105 degrees.
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sin(x/2)=±√((1-cosx)/2)
sin 105º=sin (210º/2)=±√((1-cos210º)/2)
cos 210º=cos 30º=-&#8730;3/2 (in quadrant III where cos<0)
=±&#8730;((1+&#8730;3/2)/2)
multiply by LCD 2
=±&#8730;((2+&#8730;3)/4)
take sqrt of positive root because sin 105º in quadrant II is positive
sin 105º=&#8730;(2+&#8730;3)/2