Answer:
[tex]\sf \dfrac{\sqrt{6}+\sqrt{2}}{4}[/tex]
Step-by-step explanation:
Trigonometry:
75 = 45 + 30
Sin (x + y) = Sin x *Cos y + Cos x * Sin y
Sin (45 + 30) = Sin 45 * Cos 30 + Cos 45 * Sin 30
[tex]\sf =\dfrac{1}{\sqrt{2}}*\dfrac{\sqrt{3}}{2}+\dfrac{1}{\sqrt{2}}* \dfrac{1}{2}\\\\\\=\dfrac{\sqrt{3}}{2\sqrt{2}}+\dfrac{1}{2\sqrt{2}}\\\\\\=\dfrac{\sqrt{3}*\sqrt{2}}{2*\sqrt{2}*\sqrt{2}}+\dfrac{1*\sqrt{2}}{2\sqrt{2}*\sqrt{2}}\\\\\\=\dfrac{\sqrt{6}}{2*2}+\dfrac{\sqrt{2}}{2*2}\\\\\\=\dfrac{\sqrt{6}+\sqrt{2}}{4}[/tex]
