x-(Pi/2)=t
x=t+(Pi/2)
x→ Pi/2
t→ 0
=lim_(t→ 0)(1-sin^2(t+(Pi/2))/(t+(Pi/2))*cos(t+Pi/2)=
применяем формулы приведения
=lim_(t→ 0)(1-cos^2t)/(t+(Pi/2))*(-sint)=
=lim_(t→ 0)(sin^2t)/(t+(Pi/2))*(-sint)=
=lim_(t→ 0)(-sint)/(t+(Pi/2))=0
∫ ^(Pi/6)_(0)(sin3x+cos3x)dx=
=((1/3)(-cos3x)+(1/3)sin3x)| ^(Pi/6)_(0)=
=(1/3)*0+(1/3)+(1/3)-0=2/3