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If A+B+C=180^(@), prove that: "sin"^(...

If `A+B+C=180^(@)`, prove that:
`"sin"^(2) A+"sin"^(2) B+"sin"^(2) C=2(1+cos A cos B cos C)`.

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Knowledge Check

  • (sin 2A + sin 2B + sin 2C )/( cos A + cos B + cos C -1) =

    A
    `8 sin ( A//2) sin ( B //2) sin ( C //2)`
    B
    ` 8 cos ( A//2) cos ( B //2) cos ( C//2)`
    C
    `8 sin ( A //2) cos ( B //2) cos ( C //2)`
    D
    `8 cos ( A//2) sin (B//2) sin (C //2)`

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