Question:

Simplify 1 + cos x / 1 + sec x?

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my math is rusty, summer just ended, could really use some help

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  1. 1 + cos x / 1 + sec x =

    1 + cos x / (1 + 1/cos x)  =

    1 + cos x / (cos x + 1)/cos x  =

    cos x(1 + cos x) / (cos x + 1) =

    and the above will finally simplify to "cos x", hence

    (1 + cos x) / (1 + sec x) = cos x

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