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Find the counterexample to shows that the equation sec (alpha) - cos (alpha) = sin (alpha) sec (alpha) is not an identity.

Please explain.

  • Trigonometry -

    there are many counterexamples. For instance,

    sec(pi/4) - cos(pi/4) = √2 - 1/√2
    sin(pi/4)*sec(pi/4) = 1/√2 * √2 = 1

    not equal. In fact, for any alpha not a multiple of pi, they are not equal.

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