Prove that `tantheta=(sintheta-2sin^3theta)/(2cos^3theta-costheta)`

Explanation

LHS `= frac{sin theta-2 sin ^{3} theta}{2 cos ^{3} theta-cos theta}`


`= frac{sin theta(1-2 sin ^{2} theta)}{cos theta(2 cos ^{2} theta-1)} `


`=frac{tan theta(1-2(1-cos ^{2} theta))}{2 cos ^{2} theta-1} `


`=frac{tan theta(1-2+2 cos ^{2} theta)}{2 cos ^{2} theta-1}`


`=frac{tan theta(2 cos ^{2} theta-1)}{2 cos ^{2} theta-1} `


`=tan theta`


= RHS