Question

Verify:

tanxcos(2x)=sin(2x)-tanx
using trig indentites

Answer 1

tanxcos(2x)=sinx/cosx.2cos^x-1=2cos^xsinx/cosx-sinx/cosx=sin(2x)-tanx

Answer 2

from yours, I have tanxcos(2x) +tan x = sin 2x = 2 sinx cos x

factor out: tan x (cos 2x +1) = 2sinx cos x
\[tanx = \frac{ 2sinxcosx }{ \cos2x +1 }= \frac{ 2sinx cosx }{ 2\cos^2 x}\]
right side, cancel 2cos x you get
\[tanx = \frac{ sinx }{ \cos x }\]
Hope this helps

Answer 3

I know you are not here, but I don't mind. just pick it when you come back