Question

Prove the identity:
tan x =
(cos x - cos 3x + sin 3x - sin x)/(cos x + cos 3x + sin 3x + sin x)

Answer 1

do u know
cos x +cosy =2 cos(x+y)/2 cos(x-y)/2 and other formulas of this form

Answer 2

see
cos x - cos 3x = 2 (sin (x+3x)/2 sin(3x-x)/2) = 2sin2xsinx
cos 3x + cos x = 2 (cos (x+3x)/2 cos(3x-x)/2) = 2cos2xcosx
sin 3x - sin x = 2(cos (x+3x)/2 sin(3x-x)/2 ) = 2 cos2x sinx
sin 3x + sin x = 2(sin (x+3x)/2cos(3x-x)/2 ) = 2 sin2x cosx
i hope u will be able to proceed nwo..

Answer 3

Yes. Thank you!

Answer 4

yw