解çï¼
(1)âµb2+c2=a2+â3bc
â´b^2+c^2-a^2=â3*bc.
cosA=(b^2+c^2-a^2)/2bc=â3/2,
A=â/6.
åâµsinAsinB=cos^2(C/2),
â´-1/2*[cos(A+B)-cos(A-B)]=(cosC+1)/2,
(注:å©ç¨ç§¯ååå·®å
¬å¼åcosC=2cos^2(C/2)-1,äºä¸ªå
¬å¼èå¾å°ç),åæ
cos(A-B)-cos(A+B)=cosC+1,
cos(A-B)-cos(A+B)=-cos(A+B)+1,
cos(A-B)=1,
A-B=0,
å³,A=B=â/6,
C=180-(A+B)=2â/3.
2)â7/sin30=AB/sin(180-30-15)
AB=2â7*sin45=â14.
令,ä¸è§å½¢ABC,ABè¾¹ä¸çé«ä¸ºh,
h=tan30*â14/2=â42/6.
â³ABCçé¢ç§¯=1/2*AB*h=7â3/6.
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