\sin 75\degree =\sin (45\degree +30\degree )

=\sin 45\degree \cos 30\degree +\cos 45\degree \sin 30\degree

=\dfrac{\sqrt{2} }{2} \cdotp \dfrac{\sqrt{3} }{2} +\dfrac{\sqrt{2} }{2} \cdotp \dfrac{1}{2}

=\dfrac{\sqrt{6}+\sqrt{2} }{4}