Answer
($\sqrt 3+1$)/$2\sqrt 2$ or $(\sqrt 2 + \sqrt 6)/2$
Work Step by Step
$sin 75 = sin(30+45)$
$sin(30+45)= sin 30 \times cos45 +sin 45 \times cos 30 $
$sin(30+45)=1/2 \times \sqrt 2/2 +\sqrt 2/2\times \sqrt 3/2$
This can be simplified to ($\sqrt 3+1$)/$2\sqrt 2$ or$(\sqrt 2 + \sqrt 6)/2$
