Answer: [tex]\dfrac{\sqrt2}{2}[/tex]
Step-by-step explanation:
sin 75 = sin(30 + 45) = sin30 · cos45 + cos30 · sin45
[tex]=\dfrac{1}{2}\cdot \dfrac{\sqrt2}{2}+\dfrac{\sqrt3}{2}\cdot\dfrac{\sqrt2}{2}\qquad =\dfrac{\sqrt2+\sqrt6}{4}[/tex]
sin 15 = sin(45 - 30) = sin45 · cos30 - cos45 · sin30
[tex]=\dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2}-\dfrac{\sqrt2}{2}\cdot\dfrac{1}{2}\qquad =\dfrac{\sqrt6-\sqrt2}{4}[/tex]
sin75 - sin15
[tex]=\dfrac{\sqrt2+\sqrt6}{4}-\dfrac{\sqrt6-\sqrt2}{4}[/tex]
[tex]=\dfrac{\sqrt2+\sqrt6-\sqrt6+\sqrt2}{4}\\\\=\dfrac{2\sqrt2}{4}\\\\=\dfrac{\sqrt2}{2}[/tex]
