* 4. The number of solutions to the equation $\sin ^{x} \alpha+\cos ^{x} \alpha=1\left(0<\alpha<\frac{\pi}{2}\right)$ is ( ).
(A) 0
(B) 1
(C) 2
(D) greater than 2
4. B Since $0<\sin \alpha, \cos \alpha<1$, the function $f(x)$ $=\sin ^{2} \alpha+\cos ^{x} \alpha$ is decreasing, so the original equation will not have more than one root.