已知A,B,C是三角形ABC的三个内角,且满足( sinA+sinB)^2-sin^2C= 3sinAsinB,求角C.
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已知A,B,C是三角形ABC的三个内角,且满足( sinA+sinB)^2-sin^2C= 3sinAsinB,求角C.(速求)
![已知A,B,C是三角形ABC的三个内角,且满足( sinA+sinB)^2-sin^2C= 3sinAsinB,求角C.](/uploads/image/z/18394525-37-5.jpg?t=%E5%B7%B2%E7%9F%A5A%2CB%2CC%E6%98%AF%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%E4%B8%89%E4%B8%AA%E5%86%85%E8%A7%92%2C%E4%B8%94%E6%BB%A1%E8%B6%B3%28+sinA%2BsinB%29%5E2-sin%5E2C%3D+3sinAsinB%2C%E6%B1%82%E8%A7%92C.)
(sinA+sinB)^2-sin^2C=3sinAsinB,
sin^2A+sin^2B-sin^2C=sinAsinB,
sinA/sinB+sinB/sinA-(sinC/sinA)(sinC/sinB)=1,
正弦定理a/b+b/a-(c/a)(c/b)=1,
a^2+b^2-c^2=ab
余弦定理cosC=a^2+b^2-c^2/2ab=1/2,C=60°
sin^2A+sin^2B-sin^2C=sinAsinB,
sinA/sinB+sinB/sinA-(sinC/sinA)(sinC/sinB)=1,
正弦定理a/b+b/a-(c/a)(c/b)=1,
a^2+b^2-c^2=ab
余弦定理cosC=a^2+b^2-c^2/2ab=1/2,C=60°
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