I need to prove that the equation (sin^3 + cos^3)/(1-2cos^2) = (sec - sin)/(tan-1) is true using fundamental trig function properties...any help?

Question

I am using trigonometric identities like the fundamental identities and pythagorean-rules to substitute/cancel terms until I end up with the same thing on the left of the equation as I have on the right.

Answer 1

(sin³x+cos³x)/(1-2cos²x)

=(sinx+cosx)(sin²x - sinx cosx +cos²x)/(sin²x-cos²x)=

=(sinx+cosx)(1 - sinx cosx)/[(sinx-cosx)(sinx +cosx)]=

=(1 - sinx cosx)/(sinx-cosx)=||=

=(1/cosx-sin x)/(tanx-1)=(sec x- sinx)/(tanx -1)