simplify sin7x-sin3x as a product of trig functions.
Sin7x+sin3x
To simplify the expression sin(7x) - sin(3x) as a product of trigonometric functions, you can use the identity known as the difference of angles formula for sine:
sin(A) - sin(B) = 2*sin((A - B) / 2)*cos((A + B) / 2)
Applying this identity to the expression sin(7x) - sin(3x), we have:
sin(7x) - sin(3x) = 2*sin((7x - 3x) / 2)*cos((7x + 3x) / 2)
Simplifying further:
sin(4x) = 2*sin(2x)*cos(5x)
Therefore, sin(7x) - sin(3x) simplifies to 2*sin(2x)*cos(5x).