Evaluate the following expression. (1 + sin 5y)(1 + sin (- 5y)) A)sin²5y B)cos²2y C)- sin²5y D)- cos²5y E)cos²5y

Question

Quizplus · Accepted Answer

Using the identity for the product of two sine functions, we have:

(1 + sin 5y)(1 + sin (-5y)) = 1 + sin 5y + sin (-5y) + sin 5y sin (-5y)
= 1 - cos 5y + cos 5y - cos^2 5y
= 1 - cos^2 5y

Using the identity cos^2 x + sin^2 x = 1, we have:

1 - cos^2 5y = sin^2 5y

Therefore, the expression simplifies to:

sin^2 5y

And the final answer is:

E) cos(1/2)5y

Evaluate the Following Expression. ​