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If A+B+C=180^(@),(sin2A+sin2B+sin2C)/(si...

If `A+B+C=180^(@)`,`(sin2A+sin2B+sin2C)/(sin A+sin B+sin C)=K sin(A)/(2)sin(B)/(2)sin(C)/(2)` then the value of`3K^(3)+2K^(2)+K+1` is equal to

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If A+B+C=180^(@), (sin 2A+sin 2B+sin2C)/(sinA+sinB+sinC)=k sin. (A)/(2) sin. (B)/(2) sin. (C)/(2) then the value of 3k^(3)+2k^(2)+k+1 is equal to

(sin2A + sin2B + sin2C) / (sin A + sin B + sin C) = 8sin ((A) / (2)) sin ((B) / (2)) sin ((C) / (2))

Knowledge Check

  • ( sin 2A + sin 2B + sin 2C )/( sinA + sin B + sin C ) =

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

  • If A+B+C=180^(@) , then sin2A+sin2B+sin2C=?

    A
    `4sinAsinBcosC`
    B
    `4cosAcosBcosC`
    C
    `4sinAsinBsinC`
    D
    `8sinAsinBsinC`

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    Theorem 1:sin2A+sin2B+sin2C=4sin A sin B sin C

    If A+B+C=pi , prove that : (sin 2A+sin 2B + sin 2C)/(sinA+sinB+sinC) = 8 sin(A/2) sin(B/2) sin(C/2)

    If A+B+C=180^(@), then prove that sin2A+sin2B+sin2C=4sin A sin B sin C

    If A+B+C=180^(@), show that sin2A-sin2B-sin2C=-4sin A cos B cos C

    If A+B+C=180^(@), prove that sin2A+sin2B-sin2C=4cos A cos B sin C

    sin A + sin B-sin C = 4sin ((A) / (2)) sin ((B) / (2)) cos ((C) / (2))

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