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Prove that in a triangle ABC, sinA/2 * s...

Prove that in a `triangle ABC`, `sinA/2 * sin B/2 *sin C/2 le 1/8` Also prove that equality holds if the triangle is equilateral.

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Knowledge Check

  • In any triangle ABC. sin ^(2) ""A/2 + sin ^(2) ""B/2 + sin ^(2) ""C/2 is equal to

    A
    `1- 2 cos ""A/2 cos ""B/2 cso ""C/2`
    B
    `1- 2 sin ""A/2 cos ""B/2 cos ""C/2`
    C
    `1- 2 sin ""A/2 sin ""B/2 sin ""C/2`
    D
    `1- 2 cos ""A/2 cos ""B/2 sin ""C/2`

  • In any triangle ABC, Sigma(sin^2 A+sinA+1)/(sinA) is always

    A
    9
    B
    3
    C
    27
    D
    none of these

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