Use the product-to-sum formula to find the exact value: If 2sin52.5∘sin97.5∘=2√+A√2, then A=

Question

please provide all steps for the solution

Answer 1

The product identity states that:

sin(a)sin(b) = 0.5[cos(a-b) - cos(a+b)]

Using this identity, we can plug in "a" and "b":

2sin(52.5°)sin(97.5°) = 2*0.5[cos(52.5° - 97.5°) + cos(52.5° + 97.5°)]

= [cos(-45°) + cos(150°)]

= [cos(45°) - √(3)/2] , cosine is even

= [√(2)/2 - √(3)/2]

= [√(2) -√(3)]/4

I'm not sure what 2√ refers to, but I believe you will be able to solve the question from here