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Prove that in a A B C ,sin^3A+sin^2B+si...

Prove that in a ` A B C ,sin^3A+sin^2B+sin^2Clt=9/4dot`

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`sin^(2)A+sin^(2)B+sin^(2)C`
`=1-cos^(2)A+sin^(2)B+sin^(2)C`
`=1-(cos^(2)A-sin^(2)B)+sin^(2)C`
`=1-cos(A-B)cos(A+B)+1-cos^(2)C`
`=2+cos(A-B)cos C-cos^(2)C`
`le2+cosC-cos^(2)C`. [As `cos(A-B)le1`]
`=2-((cos C-1//2)^(2)-1//4)`
`=9//4-(cos C-1//2)^(2)le9//4`
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