Question

sin 2x + cos 4x
express the above as the product of sines and cosines​

Answer 1

Answer:

sin(2x) + cos(4x) =>

sin(3x - x) + cos(3x + x) =>

sin(3x)cos(x) - sin(x)cos(3x) + cos(3x)cos(x) - sin(3x)sin(x) =>

sin(3x) * (cos(x) - sin(x)) + cos(3x) * (cos(x) - sin(x)) =>

(sin(3x) + cos(3x)) * (cos(x) - sin(x)) =>

sqrt(2) * (sin(3x) * sqrt(2)/2 + cos(3x) * sqrt(2)/2) * sqrt(2) * (cos(x) * sqrt(2)/2 - sin(x) * sqrt(2)/2) =>

2 * (sin(3x)cos(pi/4) + cos(3x)sin(pi/4)) * (cos(x)cos(pi/4) - sin(x)sin(pi/4)) =>

2 * sin(3x + pi/4) * cos(x + pi/4)