∵a是第三象限角
∴π＜a＜3π/2;
∴2π＜a+π＜5π/2;
∴cos(a+π)＞0;
∴cos(a+π)＝√(1-sin²(a+π))＝√(1-1/4)=√3/2;
∴sin(a+π/4)
=sin(a+π-3π/4)
=sin(a+π)cos(3π/4)-sin(3π/4)cos(a+π)
=(1/2)×(-√2/2)-(√2/2)×(√3/2)
=-√2/4-√6/4;
=-(√2+√6)/4;
如果本题有什么不明白可以追问,