How do you verify #cosx/(1-tanx) + sinx/(1-cotx) = sinx + cosx#?

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Answer 1 · 2018-03-25T08:06:16

#LHS=cosx/(1-tanx) + sinx/(1-cotx)#

#=cos^2x/(cosx(1-tanx)) + sin^2x/(sinx(1-cotx))#

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

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

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

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

# = sinx + cosx=RHS#