Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 years ago

Prove that cosec y = cot y sec y?

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  • Pope
    Lv 7
    2 years ago
    Best Answer

    That equation is not an identity, if that is what you mean.

    Let y = π/2.

    LHS

    = csc(y)

    = csc(π/2)

    = 1

    RHS

    = cot(y)sec(y)

    = cot(π/2)sec(π/2)

    The secant function is undefined at π/2.

    An undefined expression has been equated with 1. The equation is not an identity. Having no information on the value of y, the equation cannot be proved.

  • Como
    Lv 7
    2 years ago

    RHS

    [ cos y / sin y ] [ 1 / cos y ] = 1 / sin y = cosec y____as required

  • Raj K
    Lv 7
    2 years ago

    cosec y = cot y sec y

    RHS = cot y sec y

    =(cosy/siny)(1/cosy)

    =1/siny=cosecy=LHS Hence proved

  • cidyah
    Lv 7
    2 years ago

    cosec y= 1/sin y

    cot y sec y = (cos y/sin y)(1/cos y) = 1/sin y

    LHS = RHS

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  • 2 years ago

    LHS = cosec(y) = 1/sin(y)

    = 1/sin(y) * cos(y)/cos(y)

    = cos(y)/sin(y) * 1/cos(y)

    = cot(y) sec(y)

    = RHS

  • 2 years ago

    cosec(y) = 1/sin(y);

    and on the right-hand side,

    cot(y)sec(y) = [cos(y)/sin(y)]*[1/cos(y)] = 1/sin(y),

    the same as the left-hand side.

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