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Answer:
[tex]\frac{1}{4}[/tex] ([tex]\sqrt{6}[/tex] - [tex]\sqrt{2}[/tex] )
Step-by-step explanation:
Using the addition formula for sine
sin(A + B) = sinAcosB + cosAsinB
Given
sin165° = sin(120 + 45)° , then
sin(120 + 45)°
= sin120°cos45° + cos120°sin45°
= sin60°cos45° - cos60°sin45°
= [tex]\frac{\sqrt{3} }{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex] - [tex]\frac{1}{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex]
= [tex]\frac{\sqrt{6} }{4}[/tex] - [tex]\frac{\sqrt{2} }{4}[/tex]
= [tex]\frac{1}{4}[/tex] ( [tex]\sqrt{6}[/tex] - [tex]\sqrt{2}[/tex] )