Please answer correctly Thanks Find the value of the product

Find the value of the product. 2 sin(52.5 degree) sin(82.5 degree) Prove the identity.

Solution

Using Formula,

Cos(A-B) - Cos(A+B) = 2SinASinB

Here, A=52.5 , B=82.5

A-B = -30

A+B = 135

Therefore, 2Sin(52.5)Sin(82.5) = Cos(-30) - Cos(135) = Cos(30) - Cos(180-45)

= {sqrt(3)/2} - { - Cos(45) } = {sqrt(3)/2} + {1/sqrt(2)} = 1.5731