(sin(x)+cos(x))2=sin2(x)+2sin(x)cos(x)+cos2(x)=1+sin(2x)=¾2=9/16;
sin(2x)=2sin(x)cos(x)=-7/16;
sin(x)cos(x)=-7/32;
sin2(x)cos2(x)=49/1024.
sin6(x)+cos6(x)=sin6(x)+(1-sin2(x))3=
sin6(x)+1-3sin2(x)+3sin4(x)-sin6(x)=
1-3sin2(x)+3sin4(x)=
1+3sin2(x)(sin2(x)-1)=
1-3sin2(x)cos2(x)=1-3(49/1024)=
1-147/1024=877/1024.