在△ABC中,若sinAsinB=cos2C2,则△ABC是(  )

学习 时间:2026-03-30 08:57:46 阅读:495
在△ABC中,若sinAsinB=cos

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2026-03-30 08:57:46

△ABC中,若sinAsinB=cos2C2,∴sinAsinB= 1 + cosC2,sinAsinB=1 − cos(A+B)2,∴2sinAsinB=1-cosAcosB+sinAsinB,∴cos(A-B)=1.又-π<A-B<π,∴A-B=0,即 A=B,故△ABC是 等腰三角形,故选B.

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  • 淡定的鞋垫
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    2026-03-30 08:57:46

    △ABC中,若sinAsinB=cos2C2,∴sinAsinB= 1 + cosC2,sinAsinB=1 − cos(A+B)2,∴2sinAsinB=1-cosAcosB+sinAsinB,∴cos(A-B)=1.又-π<A-B<π,∴A-B=0,即 A=B,故△ABC是 等腰三角形,故选B.

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