Question 1043835

{{{(cos^3(x)+sin^3(x))/(cos(x)+sin(x))=1-sin(x)cos(x)}}}


recall: {{{a^3+b^3=(a+b)(a^2-ab+b^2)}}}


{{{((cos(x)+sin(x))(cos^2(x)-cos(x)sin(x)+sin^2(x)))/(cos(x)+sin(x))=1-sin(x)cos(x)}}}


{{{(cross((cos(x)+sin(x)))(cos^2(x)-cos(x)sin(x)+sin^2(x)))/cross((cos(x)+sin(x)))=1-sin(x)cos(x)}}}


{{{cos^2(x)-cos(x)sin(x)+sin^2(x)=1-sin(x)cos(x)}}}.....rearrange left side


{{{sin^2(x)+cos^2(x)-sin(x)cos(x)=1-sin(x)cos(x)}}}......since {{{sin^2(x)+cos^2(x)=1}}}, we have


{{{1-sin(x)cos(x)=1-sin(x)cos(x)}}}