Answer:
[tex]\frac{1}{4}[/tex] ([tex]\sqrt{2}[/tex] - [tex]\sqrt{6}[/tex] )
Step-by-step explanation:
using the identity
• sin(x - y) = sin x cos y - cos xsin y
and the exact values
sin45° = cos45° = [tex]\frac{\sqrt{2} }{2}[/tex] , sin30° = [tex]\frac{1}{2}[/tex] , cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]
given
sin(- 15)°
= sin(30 - 45)°
= sin30°cos45° - cos30°sin45°
= [tex]\frac{1}{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex] - [tex]\frac{\sqrt{3} }{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex]
= [tex]\frac{\sqrt{2} }{4}[/tex] - [tex]\frac{\sqrt{6} }{4}[/tex]
= [tex]\frac{1}{4}[/tex] ([tex]\sqrt{2}[/tex] - [tex]\sqrt{6}[/tex] )
