Example 6. The smallest positive angle $x$ that satisfies the equation $\sin \left(2 x+45^{\circ}\right)=\cos \left(30^{\circ}-x\right)$ is
(A) $60^{\circ}$;
(B) $45^{\circ}$;
(C) $30^{\circ}$;
(D) $25^{\circ}$; (E) $15^{\circ}$.
Solve by substituting $x=15^{\circ}$, $\sin 75^{\circ}=\cos 15^{\circ}$ is correct, so the answer is (E).