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

1 Answer
May 19, 2018

Answer:

#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#