How do you verify #(2cot2x)/(cosx-sinx)=cscx+secx#?

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Answer 1 · 2016-11-15T07:53:49

#LHS=(2cot2x)/(cosx-sinx)#

#=(2cos2x)/(sin2x(cosx-sinx))#

#=(cancel2(cos^2x-sin^2x))/(cancel2sinxcosx(cosx-sinx))#

#=((cancel(cosx-sinx))(cosx+sinx))/(sinxcosx(cancel(cosx-sinx)))#

#=cosx/(sinxcosx)+sinx/(sinxcosx)#

#=cscx+secx#

verified

Not valid when #cosx=sinx " "i.e.x=npi+pi/4#
#n in ZZ#