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Thread: trigonometry proof help.

  1. #1
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    trigonometry proof help.

    2cosx - secx = - tanx

    thank you in advance.

    i need to solve the equation and give an answer in radians.
    Last edited by starrytulips143; Dec 1st 2009 at 04:03 PM. Reason: make it more clear.
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  2. #2
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    The equation you wrote was:

    $\displaystyle 2cos(x)-sec(x)=-tan(x)$



    I'm not sure if this is true. Consider the angle $\displaystyle \frac{\pi}{3}$

    $\displaystyle 2cos\left(\frac{\pi}{3}\right)-sec\left(\frac{\pi}{3}\right)=-tan\left(\frac{\pi}{3}\right)$

    The left side becomes:
    $\displaystyle 2(.5)-2=-1$

    The right side becomes:

    $\displaystyle tan(\frac{\pi}{3})=\sqrt{3}\approx 1.73$
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  3. #3
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    Hello starrytulips143
    Quote Originally Posted by starrytulips143 View Post
    2cosx - secx = - tanx

    thank you in advance.

    i need to solve the equation and give an answer in radians.
    Here are the steps to take; I'll leave the details to you:

    • Using $\displaystyle \sec x = \frac{1}{\cos x}$ and $\displaystyle \tan x = \frac{\sin x}{\cos x}$, express everything in terms of sine and cosine.


    • Multiply both sides by $\displaystyle \cos x$ to get rid of fractions.


    • Then use $\displaystyle \cos^2x+\sin^2x=1$ to express everything in terms of $\displaystyle \sin x$.


    • Re-arrange as a quadratic in $\displaystyle \sin x$.


    • Factorise. You should get:

    $\displaystyle (2\sin x+1)(\sin x -1)=0$
    Can you complete it now?

    Grandad
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