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Thread: Verifying/proving help?

  1. #1
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    Verifying/proving help?

    5 sin(x+arctan(4/3)) = 3 sin x + 4 cos x

    (arctan is the inverse tangent)
    I'm really having trouble trying to prove this. I'm mainly stuck with what to do with the inverse tangent.
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  2. #2
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    Quote Originally Posted by Rinnie View Post
    5 sin(x+arctan(4/3)) = 3 sin x + 4 cos x

    (arctan is the inverse tangent)
    I'm really having trouble trying to prove this. I'm mainly stuck with what to do with the inverse tangent.
    let \theta = \arctan\left(\frac{4}{3}\right) ... using right triangle ratios, \sin{\theta} = \frac{4}{5} and \cos{\theta} = \frac{3}{5}


    sum identity for sine ...

    5 \sin(x + \theta) = 5[\sin{x}\cos{\theta} + \cos{x}\sin{\theta}]

    substitute in the values for \cos{\theta} and \sin{\theta} and finish it.
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  3. #3
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    Then, of course, use sin(x+ \theta)= cos(x)cos(\theta)- sin(x)sin(\theta).
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  4. #4
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    Quote Originally Posted by HallsofIvy View Post
    Then, of course, use \cos(x+ \theta)= \cos(x)\cos(\theta)- \sin(x)\sin(\theta).
    fify
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