Question

докажите тождество: (sin^3a+cos^3a):(sin a +cos a)+sin a*cos a =1

Answer 1

$frac{sin^3a+cos^3a}{sina+cosa}+sinacosa=frac{(sina+cosa)(sin^2a-sinacosa+cos^2a)}{sina+cosa}+sinacosa=\=sin^2a-sinacosa+cos^2a+sinacosa=sin^2a+cos^2a=1$