Answer:
[tex]\frac{2+\sqrt{3} }{2}[/tex]
Step-by-step explanation:
Using the product to sum formula
sinxcosy = [tex]\frac{1}{2}[/tex] [ sin(x + y) + sin(x - y) ] , then
2sinxcosy = sin(x + y) + sin(x - y)
Given
2sin75°cos15° ← with x = 75 and y = 15 , then
= sin(75 + 15) + sin(75 - 15)
= sin90° + sin60°
= 1 + [tex]\frac{\sqrt{3} }{2}[/tex]
= [tex]\frac{2+\sqrt{3} }{2}[/tex]