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If A+B+C =pi , then the value of determi...

If `A+B+C =pi` , then the value of determinant `|{:(sin^2A,cotA,1),(sin^2B,cotB,1),(sin^2C,cotC,1):}|` is equal to

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For any triangleABC, the value of determinant |[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,cotC,1]| is:

If A+B+C=pi, then the value of |[sin(A+B+C),sin(A+C),cosC],[-sinB,0,tanC],[cos(A+B),tan(B+C),0]|is equal to (a)0 (b) 1 (c) 2sinBtanAcosC (d) none of these

Knowledge Check

  • If A+B+C=pi , then the value of determinant |{:(sin^(2)A, cotA,1),(sin^(2)B,cotB,1),(sin^(2)C,cot C,1):}| is equal to

    A
    0
    B
    1
    C
    `-1`
    D
    None of these

  • In a Delta ABC , a, b, c are sides and A, B, C are angles opposite to them, then the value of the determinant |(a^(2),b sin A,c sin A),(b sin A,1,cos A),(c sin A,cos A,1)| , is

    A
    0
    B
    1
    C
    2
    D
    3

  • If A, B, C are the angles of a triangle, then the determinant Delta = |(sin 2 A,sin C,sin B),(sin C,sin 2B,sin A),(sin B,sin A,sin 2 C)| is equal to

    A
    1
    B
    `-1`
    C
    `sin A + sin B + sin C`
    D
    none of these

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