1.(a+b+c)(a+c-b)=(2+根號(hào)3)ac
(a+c)^2-b^2=(2+根號(hào)3)ac
a^2+2ac+c^2-b^2=2ac+√3ac
a^2+c^2-b^2=√3ac
余弦定理
cosB=(a^2+c^2-b^2)/2ac=√3/2銳角三角形
B=30°
2.sinC=sin(150°-A)=sin150°cosA-cos150°sinA=1/2cosA+√3/2sinA
cosA+sinC=3/2cosA+√3/2sinA=根號(hào)6/2
3/2cosA+√3/2sinA=√3sin(A+60°)=√6/2
sin(A+60°)=√2/2A+60°=135°A=75° C=75°
sinA=sin(30°+45°)=(√6+√2)/4
正弦定理
a/sinA=b/sinB
a=2 c=2
S=1/2*ac*sinB=1
3. B=30°
cosA+sinC
=cos(150°-C)+sinC
=cos150°cosC+sin150°sinC+sinC
=-√3/2cosC+3/2sinC
=√3sin(C-60°)60°0°00<√3sin(C-60°)<√3/2
cosA+sinC的范圍(0,√3/2)那啥，第三問(wèn)cosA+sinC= - √3/2cosC+3/2sinC=√3sin(C-30°)B=30°A+C=150°銳角三角形C<90° A<90°A=150°-C 150°-C<90°C>60°所以 60°