1.因为是第二象限角,故cosa=-3/5
cos(α -π/3)
=cosacos60+sinasin60
=-3/5 * 1/2 +4/5 *根号3/2
=(4根号3-3)/10
2.由题意：sinx/2 +cosx=sinx/2 +1-2*(sinx/2)^2=1
那么 2(sinx/2)^2-sinx/2=0
则sinx/2 =0或sinx/2=1/2
那么x/2 =kπ或π/6 + 2kπ或5π/6 +2kπ
那么x=2kπ或π/3 +4kπ或5π/3+4kπ.