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Math Help - Prove that tan(45 + A)........

  1. #1
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    Prove that tan(45 + A)........

    Prove that tan(45+A) = cosA + sinA/cosA - sinA


    I converted tan(45+A) into 1+tanA/1 - tanA


    but i dont know what to do next? Im sure its just a small thing but i just cant get it! Some help please!
    Last edited by milan; March 3rd 2008 at 01:16 PM.
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  2. #2
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    \tan \left( \frac{\pi}{4} + A \right) = \frac{ \tan( \frac{\pi}{4} ) + \tan A}{1 -  \tan( \frac{\pi}{4}) \tan A }

    \Rightarrow \ \ \frac{ 1 + \tan A}{1 - \tan A }

    \Rightarrow \ \ \frac{ 1 + \frac{\sin A}{\cos A}}{1 - \frac{\sin A}{\cos A} } \ \ = \ \ \frac{ 1 + \frac{\sin A}{\cos A}}{1 - \frac{\sin A}{\cos A} } \times \frac{\cos A }{\cos A }

    \Rightarrow \frac{ \cos A + \sin A}{\cos A - \sin A}
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