StudyDaddy Geometry

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QUESTION

Feb 03, 2017

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)##

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