Question

(tan x) / (sin x- cos x) = (sin^2 x + (sin x)(cos x))/ (cos x - 2 cos ^3 x) (working from one side to the other.)

Answer 1

you want to prove that it equals to that?

Answer 2

Multiply bot sides with (sinx + cosx) and you'll get the following:

\[= (tanx(sinx+cosx))/(sinx-cosx)(sinx+cosx)\]
\[= [(sinx/cosx)(sinx+cosx)]/(\sin^2x-\cos^2x)\]
\[= [(\sin^2x +cosxsinx)/cosx]/(1-\cos^2x-\cos^2x)\]


\[= (\sin^2x + cosxsinx)/cosx(1-2\cos^2x)\]

\[= (\sin^2x + cosxsinx)/(cosx-2\cos^3x)\]

^_^