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Math Help - Hard Trig Proof

  1. #1
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    Hard Trig Proof

    tanxsinx + cosx = \frac{1}{cosx}

    RS = \frac{1}{cosx}

    = \frac{tanx}{sinx}

    = \frac{sinx}{sinxcosx}

    = \frac{sinxtanx}{sinxcosxtanx}

    = \frac{sinxtanx}{sinxsinx}

    = \frac{sinxtanx}{sin^2x}

    = \frac{sinxtanx}{1 - cos^2x}

    What do I do from here? Is there a simpler way of solving this?
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  2. #2
    MHF Contributor
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    \tan{x}\sin{x}+\cos{x} =

    \frac{\sin{x}}{\cos{x}} \cdot \sin{x} + \cos{x} \cdot \frac{\cos{x}}{\cos{x}} =

    \frac{\sin^2{x}}{\cos{x}} + \frac{\cos^2{x}}{\cos{x}} =

    put them together and finish.
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  3. #3
    Super Member bigwave's Avatar
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    just to mention about solving identities this one being an example

    try to get everything into sin and cos. then the identities are easy to see.

    keepimg tan in this one made things more difficult.
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  4. #4
    Senior Member pacman's Avatar
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    tan x sin x + cos x = 1/cos x

    tan x ( tan x cos x) + cos x =

    tan^2 x cos x + cos x =

    cos x (tan^2 x + 1) =

    cos x(sec^2 x) =

    cos x (1/cos x)(1/cos x) = ?



    voila!
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