Question

express as a single fraction the exact value of sin 75

Answer 1

\[\sin75=\sin(30+45)=\sin30\cos45+\cos30\sin45\]

Answer 2

sin75=sin(45+30)=sin45.cos30+cos45.sin30=(\[\sqrt{3}/2+1/2\])\[\div\]\[\sqrt{2}\]
=(sqrt(3)+1)/(2*sqrt(2)).

Answer 3

\[=\frac{1}{2}(\frac{\sqrt{2}}{2})+\frac{\sqrt{3}}{2}(\frac{\sqrt{2}}{2})=\frac{\sqrt{2}+\sqrt{6}}{4}\]