
Arturo O. answered 05/08/17
Tutor
5.0
(66)
Experienced Physics Teacher for Physics Tutoring
Use the trigonometric identity
sin(a) + sin(b) = 2 cos[(a - b)/2] sin[(a + b)/2]
You can also use the property that
sin(-a) = -sin(a)
Then
sin2x - sin5x = sin2x + sin(-5x) = 2 cos[(2x + 5x)/2] sin[(2x - 5x)/2]
sin2x - sin5x = 2 cos(7x/2) sin(-3x/2) = -2 cos(7x/2) sin(3x/2)