Question

Prove or disprove the following identity:

(sin(10x))/(sin(x)+sin(9x)) = (cos(5x))/(cos4x))

Answer 1

sin(x)+sin(9x) = 2sin(5x)cos(4x), so

sin(10x)/(2sin(5x)cos(4x)) = cos(5x)/cos(4x)
sin(10x)cos(4x) = 2cos(5x)sin(5x)cos(4x)
sin(10x)cos(4x) = sin(10x)cos(4x)
QED