How do you verify #(sin^3x+cos^3x)/(sinx+cosx)=1-sinxcosx#?

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Apr 22, 2016

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Expansion of a cubic #a^3+b^3=(a+b)(a^2-ab+b^2)#
#(sin^3x+cos^3x)/(sinx+cosx)=((sinx+cosx)(sin^2x-sinxcosx+cos^2x))/(sinx+cosx)#
#=sin^2x-sinxcosx+cos^2x#
Identity: #sin^2x+cos^2x=1#
#=sin^2x+cos^2x-sinxcosx#
#=1-sinxcosx#

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