write the expression sin4xsin5x as a sum or difference of trigonometric functions
To express the expression sin(4x)sin(5x) as a sum or difference of trigonometric functions, we can use the product-to-sum identities.
The product-to-sum identity is given by: sin(A)sin(B) = (1/2)[cos(A - B) - cos(A + B)]
Let's apply this identity to sin(4x)sin(5x):
sin(4x)sin(5x) = (1/2)[cos(4x - 5x) - cos(4x + 5x)]
Now, simplifying the expression:
sin(4x)sin(5x) = (1/2)[cos(-x) - cos(9x)]
= (1/2)[cos(x) - cos(9x)]
Therefore, sin(4x)sin(5x) can be written as the sum or difference of trigonometric functions as (1/2)[cos(x) - cos(9x)].