Sin³x-cos³x=1+(sin2x)/2;⇒
(sinx-cosx)(sin²x+sinx·cosx+cos²x)=1+(sin2x)/2;⇒
(sinx-cosx)(1+(sin2x)/2)=1+(sin2x)/2;⇒
sinx-cosx=1;⇒
sinx=2tg(x/2)/(1+tg²(x/2));x≠π(2k+1);k∈Z;
cosx=(1-tg²(x/2))/(1+tg²(x/2);
tg(x/2)=t;⇒
2t/(1+t²)-(1-t²)/(1+t²)=1;
2t-1+t²=1+t²;⇒
2t=2;⇒
t=1;⇒tgx/2=1;⇒x/2=π/4+kπ;k∈Z;
x=π/2+2kπ;k∈Z;