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Prove that in a A B C ,sin^2A+sin^2B+si...

Prove that in a ` A B C ,sin^2A+sin^2B+sin^2C<=9/4dot`

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`cos2A=1-2sin^2A`
`sin^2A=(1-cos2A)/2`
`=(1-cos2A)/2+(1-cos2B)/2+sin^2C`
`=1+sin^2C-1/2(cos2A+cos2B)`
`=1+sin^2C-1/2(2cos(A_B)*cos(A-B))`
`=1+sin^2C-cos(A+B)*cos(A-B)`
`A+B+C=pi`
`A+B=pi-C`
...
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