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    Simplifying and Factoring Trigonometric Expressions

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    1. Simplify: sin^2(x)/sec^2(x)-1

    2. Factor and simplify: cos^2(x)-sin^2(x)cos^2(x)

    3. Perform the addition and simplify: 1/1+sinx + 1/1-sinx

    4. Simplify: sec^4(x) + sec^2(x)-2

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    Solution Preview

    1. sec^2(x)-1=1/cos^2(x) - 1=(1-cos^2(x))/cos^2(x)=sin^2(x)/cos^2(x) so sin^2(x)/(sec^2(x)-1)=cos^2(x).
    2.We can write it as ...

    Solution Summary

    This shows how to simplify a variety of trigonometric expressions.