Find the value of the product. 2 sin (52.5°) sin (97.5°)

2sin (52.5) sin (97.5) = [√ (2) + √ (3) ] / 2

=1.5731

Step-by-step explanation:

As we the trigonometric identity of the product of sines

sin (x) sin (y) = [cos (x-y) - cos (x+y) ] / 2

2sin (x) sin (y) = [cos (x-y) - cos (x+y) ]

putting values of x and y

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

=cos (45) - cos (150)

= 1/√ (2) - (-√ (3) / 2)

= √ (2) / 2 + √ (3) / 2)

= [√ (2) + √ (3) ] / 2

=1.5731