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Math Help - Proving the greatest value for Tan

  1. #1
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    Proving the greatest value for Tan

    I'm revising for an exam and I'm stuck on part of my revision question.
    I have proven that Tan\theta=\frac{5sin\alpha}{13-5cos\alpha} in the given question, but now I have to prove that tan\theta has the greatest value at cos\alpha=\frac{5}{13}
    Can anyone help me prove it?
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  2. #2
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    Quote Originally Posted by thepopasmurf View Post
    I'm revising for an exam and I'm stuck on part of my revision question.
    I have proven that Tan\theta=\frac{5sin\alpha}{13-5cos\alpha} in the given question, but now I have to prove that tan\theta has the greatest value at cos\alpha=\frac{5}{13}
    Can anyone help me prove it?
    Use calculus to find the maximum of y = \frac{5sin\alpha}{13-5cos\alpha}:

    Solve \frac{dy}{d \alpha} = 0 etc.
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  3. #3
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    I thought about using calculus but I'm fairly sure it can be done without it. The book stays away from calculus until differential equations
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  4. #4
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    I'm sorry, but does anyone have any ideas?
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