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a^2 /b^2 = sinAcosB / (coaAsinB)
根据正弦定理：a/b = sinA/sinB,a^2/b^2 = (a/b)^2 = (sinA/sinB)^2 = sin^2A / sin^2B
∴sin^2A / sin^2B = sinAcosB / (coaAsinB)
sin^2A / sin^2B - sinAcosB / (coaAsinB) = 0
sinA/sinB (sinA/sinB - cosB / coaA ) = 0
sinA/sinB * (sinAcosA-sinB cosB )/ (sinBcoaA ) = 0
sinA/(sin^2B cosA) * (sinAcosA-sinB cosB ) = 0
sinA/(2sin^2B cosA) * (2sinAcosA-sinB cosB ) = 0
sinA/(2sin^2B cosA) * (sin2A-sin2B ) = 0
∵sinA/(2sin^2B cosA) ≠ 0,∴sin2A-sin2B =0
即：2A=2B,或2A=π-2B
A=B,或A+B=π/2
等腰三角形,或直角三角形
根据正弦定理：a/b = sinA/sinB,a^2/b^2 = (a/b)^2 = (sinA/sinB)^2 = sin^2A / sin^2B
∴sin^2A / sin^2B = sinAcosB / (coaAsinB)
sin^2A / sin^2B - sinAcosB / (coaAsinB) = 0
sinA/sinB (sinA/sinB - cosB / coaA ) = 0
sinA/sinB * (sinAcosA-sinB cosB )/ (sinBcoaA ) = 0
sinA/(sin^2B cosA) * (sinAcosA-sinB cosB ) = 0
sinA/(2sin^2B cosA) * (2sinAcosA-sinB cosB ) = 0
sinA/(2sin^2B cosA) * (sin2A-sin2B ) = 0
∵sinA/(2sin^2B cosA) ≠ 0,∴sin2A-sin2B =0
即：2A=2B,或2A=π-2B
A=B,或A+B=π/2
等腰三角形,或直角三角形
1年前
9
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