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Math Help - Help with simplifying trigonometric identities.

  1. #1
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    Help with simplifying trigonometric identities.

    I need help simplifying this:

    tanX(cosX-cotX)
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  2. #2
    Senior Member
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    Hi Andrew Jensen

    Try :

    \tan x=\frac{\sin x}{\cos x}

    \cot x=\frac{\cos x}{\sin x}
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  3. #3
    Super Member

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    Hello, Andrew Jensen!

    I must assume that you know some basic identities . . .


    Simplify: . \tan x(\cos x - \cot x)

    Multiply: . \tan x\!\cdot\!\cos x - \tan x\!\cdot\!\cot x

    We know that: . \tan x \,=\,\frac{\sin x}{\cos x} \qquad \cot x \,=\,\frac{1}{\tan x}


    So we have: . \frac{\sin x}{{\color{red}\rlap{/////}}\cos x}\cdot{\color{red}\rlap{/////}}\cos x \;-\; {\color{red}\rlap{/////}}\tan x\cdot\frac{1}{{\color{red}\rlap{/////}}\tan x} \;\;=\;\;\sin x - 1

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