2.3.3 * In $\triangle A B C$, if $(\sin A+\sin B)(\cos A+\cos B)=2 \sin C$, then ( ).
(A) $\triangle A B C$ is an isosceles triangle, but not necessarily a right triangle
(B) $\triangle A B C$ is a right triangle, but not necessarily an isosceles triangle
(C) $\triangle A B C$ is neither an isosceles triangle nor a right triangle
(D) $\triangle A B C$ is both an isosceles triangle and a right triangle