AHSME 1974 Problem 22

The minimum of $\sin\frac{A}{2}-\sqrt{3}\cos\frac{A}{2}$ is attained when $A$ is $\mathrm{(A)\ } -180^\circ \mathrm{(B) \ }60^\circ \mathrm{(C) \ } 120^\circ \mathrm{(D) \ } 0^\circ \mathrm{(E) \ }\text{none of these}$