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Thread: Simplifying trigonometric expression

  1. #1
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    Question Simplifying trigonometric expression

    Hi,

    I hope someone can help me properly simplify the following expression:

    Simplifying trigonometric expression-18789653_1424089084313848_1372609242_o.jpg

    The solution is apparently
    Simplifying trigonometric expression-screen-shot-2017-06-02-3.19.42-pm.png

    Sincerely,
    Olivia
    Attached Thumbnails Attached Thumbnails Simplifying trigonometric expression-18901273_1424085167647573_918297707_o.jpg  
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  2. #2
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    Re: Simplifying trigonometric expression

    $\begin{align*}\dfrac{\sin(f+g)+\sin(f-g)}{\cos(f+g) + \cos(f-g)} & = \dfrac{\sin f \cos g + \cancel{\sin g \cos f} + \sin f \cos g + \cancel{- \sin g \cos f}}{\cos f \cos g + \cancel{-\sin f \sin g} + \cos f \cos g + \cancel{\sin f \sin g}} \\ & = \dfrac{\cancel{2}\sin f \cancel{\cos g}}{\cancel{2}\cos f \cancel{\cos g}} \\ & = \tan f\end{align*}$

    Because we cancelled $\cos g$ from top and bottom, we need $\cos g \neq 0$. Because $\tan f$ is not defined when $\cos f = 0$, there is no need to specifically identify that as a condition.

    You just missed the last steps where you cancel the 2's and cancel the $\cos g$ from top and bottom.
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  3. #3
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    Re: Simplifying trigonometric expression

    Ok that makes perfect sense. Thanks for you help!
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