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#

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