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29 June, 22:56

Cot x sec4x = cot x + 2 tan x + tan3x

Is this equation or identity?

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Answers (2)
  1. 30 June, 00:35
    0
    The correct answer is:

    An equation.

    Explanation:

    An equation is a statement that is true for particular values of the variable. An identity, however, is a statement that is true for any values of the variable.

    If we use 60° as x, the left hand side of the equation gives us - 1.15. The right hand side gives us 4.04. These are not equal, so this cannot be an identity.
  2. 30 June, 02:36
    0
    It is an equation:

    here is the proof:

    The key to this one is that sec^2 (x) = 1 + tan^2 (x).

    So the left side is

    cot (x) (1 + tan^2 (x)) (1 + tan^2 (x))

    Expanding this term by term you get

    cot (x) + 2 cot (x) tan^2 (x) + cot (x) tan^4 (x),

    but since cot (x) tan (x) = 1, that turns into

    cot (x) + 2 tan (x) + tan^3 (x),

    which is the same as the right side.
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