Basic pre-calc/trig...help with solving an equation?

tanxsinx=secx-cosx>>>> (sinx/cosx)(sinx)=1/cosx-cosx multiply both sides by cosx, so cosx(sinx/cosx)(sinx)=cosx(1/cosx-cosx) >>>>>>> sinx^2=1-cosx^2, and we can transform either side to show they are equal . Either 1-cosx^2=1-cosx^2 or sinx^2=sinx^2