Math

Which of the following counterexamples proves that sinxtanx=cosx is not a trigonometric identity? Select all that apply.

-2π
-3π
-3π/4
-π/4

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  1. method1:
    simply substitute each value into the equation to each if
    it satisfies.
    If the given value satisfies the equation, it clearly cannot be
    used as a counter-example.
    If the given value does not satisfy the equation ........

    method 2: actually solve the given equation to see which
    values are solutions.
    sinxtanx = cosx
    sinx(sinx/cos) = cosx
    sin^2 x = cos^2 x
    cos^2 x - sin^2 x = 0
    cos(2x) = 0

    2x = ± π/2 , ± because of the symmetry of the cosine curve in the y-axis

    x = ± π/4
    since cos 2x has a period of π
    +π/4 - π = -3π/4 is also solution

    Clearly since -π/4 and -3π/4 are in your list and they satisfy
    the equation they CANNOT be used as counterexamples.

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