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Math Help - Inverse trig - please help!!!

  1. #1
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    Exclamation Inverse trig - please help!!!

    How exactly do I solve arctan(3x) + arctan(x) = pi/4???
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  2. #2
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    Quote Originally Posted by xwrathbringerx View Post
    How exactly do I solve arctan(3x) + arctan(x) = pi/4???
    You might try taking the tangent of both sides:
    tan(arctan(3x)+ arctan(x))= tan(\pi/4)= 1.

    On the left you will need the identity: tan(a+b)= \frac{tan(a)+ tan(b)}{1- tan(a)tan(b)}.
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  3. #3
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    ummm does tan (a) = 3x and tan(b) = x with me eventually getting the quadratic equation 3x^2 + 4x -1 = 0?
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  4. #4
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    Quote Originally Posted by xwrathbringerx View Post
    How exactly do I solve arctan(3x) + arctan(x) = pi/4???
    hi

    \tan^{-1} 3x+\tan^{-1} x=\frac{\pi}{4}

    \tan^{-1} 3x=\alpha\Rightarrow \tan \alpha=3x

    \tan^{-1} x=\beta \Rightarrow \tan \beta=x

    \alpha+\beta=\frac{\pi}{4}

    \tan (\alpha+\beta)=\tan \frac{\pi}{4}

    \frac{\tan \alpha+\tan \beta}{1-\tan \alpha\tan \beta}=1

    \frac{3x+x}{1-3x^2}=1

    solve 3x^2+4x-1=0
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