b/sinB=a/sinA=2b\x0d
sinB=1/2\x0d
B=30°,或150°
所以:cos[(B/2)-45°]=cos(-30°)=√(3)/2\x0d
或,cos[(B/2)-45°]=cos(30°)=√(3)/2\x0d
cosA+sinC=sin(90°-A)+sinC=2sin[45°-(A-C)/2]*cos[45°-(A+C)/2]\x0d
=2sin[45°-(A-C)/2]*cos[(B/2)-45°]\x0d
=√(3)*sin[45°-(A-C)/2]
當(dāng)(A-C)/2=-45°, C-A=90°,cosA+sinC為最大值:√(3)
A-C=(A+C)-2C=180°-B-2C<180°-B≤180°-30°\x0d
(A-C)/2<75°\x0d
45°-(A-C)/2>45°-75°\x0d
45°-(A-C)/2>-30°\x0d
所以:cosA+sinC>√(3)*sin(-30°)\x0d
cosA+sinC>-√(3)/2\x0d
綜合以上,得: -√(3)/2