How to prove?

Question

#(1+secx)/(tan^(2)x)=(cosx)/(1-cosx)#

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Answer 1 · 2018-03-03T05:03:20

#=L.H.S#

#=(1+secx)/(tan^2x)#

#=((1+1/cosx)/(sin^2x/cos^2x))#

#=(cosx+1)/cosx xxcos^2x/sin^2x#

#=((cosx+1)cosx)/sin^2x#

#=((cosx+1)cosx)/((1-cos^2x))#

#=(cancelcolor(blue)((cosx+1))cosx)/(cancelcolor(blue)((1+cosx))(1-cosx))#

#=cosx/(1-cosx)#

#=R.H.Scolor(green)([Proved.])#

Answer 2 · 2018-03-03T05:07:32

See below

#(1+secx)/tan^2x=cosx/(1-cosx)#

#(1+secx)/(1-sec^2x)=cosx/(1-cosx)#

#(1+secx)/((1+secx)(1-secx))=cosx/(1-cosx)#

#1/(1-secx)=cosx/(1-cosx)#

#1/(cosx/cosx-1/cosx)=cosx/(1-cosx)#

#1/((cosx-1)/cosx)=cosx/(1-cosx)#

#cosx/(1-cosx)=cosx/(1-cosx)#