How do you prove: ##cosx- (cosx/(1-tanx))= (sinxcosx)/(sinx-cosx)##?

##(sinx cosx) / (sinx – cosx) = cosx – [(cosx) / ( 1 – tan x)]##

##(sinx cosx) / (sinx – cosx) = cosx – {(cos x ) / [ 1 – ( sinx / cosx)]} ##

##(sinx cosx) / (sinx – cosx) = cosx – {(cosx) / [(cosx – sinx) / cosx]}##

##(sinx cosx) / (sinx – cosx) = cosx – {(cosx) [cosx / (cosx – sinx)]}##

##(sinx cosx) / (sinx – cosx) = cosx – [ (cos ^2 x) / (cosx – sinx)]##

##(sinx cosx) / (sinx – cosx) = [cosx( cosx – sinx ) – (cos ^2 x) ] / (cosx – sinx)##

##(sinx cosx) / (sinx – cosx) = (cos ^2 x – cosx sinx – cos ^2 x ) / (cosx – sin x)##

##(sinx cosx) / (sinx – cosx) = – (cosx sinx) / ( cosx – sinx )##

##(sinx cosx) / (sinx – cosx) = – (cosx sinx) / [ – ( sinx – cosx)]##

##(sinx cosx) / (sinx – cosx) = (-cosx sinx) / [ – ( sinx – cosx)]##

##(sinx cosx) / (sinx – cosx) = (cosx sinx) / ( sinx – cosx)##