Experience the power of community-driven knowledge on IDNLearn.com. Get the information you need from our community of experts who provide accurate and comprehensive answers to all your questions.
Sagot :
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] )
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.
