How do you simplify (cos4x-cos2x)/(sin 4x + sin 2x)?

1 Answer
May 19, 2018

color(crimson)(=> - tan x

Explanation:

(cos 4x - cos 2x) / (sin 4x + sin 2x)

cos C -cos D = -2 sin (C+D)/2 sin (C-D)/2

sin C +sin D = 2 sin (C +D)/2 cos (C -D)/2

Nr = -2 sin ((4x+2x)/2) * sin ((4x-2x)/2)

Nr = -2 sin 3x * sin x

Dr = 2 sin ((4x+2x)/2) * cos((4x-2x)/2)

Dr = 2 sin3x * cos x

(Nr) / (Dr) =- (cancel2 cancel(sin 3x) * sin x) / (cancel2 cancel(sin 3x) * cos x)

color(crimson)(=> - sin x / cos x = - tan x