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If alpha, beta, gamma are three distinct...

If `alpha, beta, gamma` are three distinct real numbers such than `0 < alpha, beta, gamma < pi/2,` then `tan (alpha-beta) + tan (beta-gamma)+tan(gamma-alpha)` is equal to :

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Knowledge Check

  • If alpha, beta, gamma are three distinct real numbers such that 0 lt alpha, beta, gamma lt pi//2 , then tan(alpha-beta)+tan(beta-gamma)+tan(gamma-alpha) is equal to :

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

  • Let alpha, beta, gamma are distinct real numbers. The points with position vectors alpha i + beta j + gamma k , beta i + gamma j + alpha k , gamma i + alpha j + beta k

    A
    from a right angle triangle
    B
    form a scalene triangle
    C
    form an equilateral triangle
    D
    are collinear

  • If alpha, beta, gamma are three real numbers, then cos^(2)(beta-gamma)+cos^(2)(gamma-alpha)+cos^(2)(alpha-beta)-2cos(beta-gamma)cos(gamma-alpha)cos(alpha-beta) is equal to

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    B
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    C
    `-1`
    D
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