Question

Express the given product as a sum or difference containing only sines or cosines.

sin (7x) sin (4x)
sin (7x) sin (4x) = _______ Simplify your answer.)

Answer 1

The product sin(7x) sin(4x) can be simplified using product-to-sum identities, resulting in the expression ½(cos(3x) - cos(11x)).

Step-by-step explanation:

The product of sin(7x) sin(4x) can be expressed as a sum or difference using trigonometric identities.

We use the product-to-sum identities, specifically the identity sin A sin B = ½(cos(A-B) - cos(A+B)).

Applying this identity to sin(7x) sin(4x), we get:

• ½(cos(7x-4x) - cos(7x+4x))
• ½(cos(3x) - cos(11x))

Therefore, the expression sin(7x) sin(4x) sin(7x) sin(4x) simplifies to ½(cos(3x) - cos(11x)).