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Math Help - trigonometry

  1. #1
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    Smile trigonometry

    Hi guys
    could you please help me to prove cos3a-cos7a/sin7a+sin3a=tan2a
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  2. #2
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by bahram View Post
    Hi guys
    could you please help me to prove cos3a-cos7a/sin7a+sin3a=tan2a
    Just to clarify the problem, is this correct?

    cos(3a) - \frac{cos(7a)}{sin(7a)} + sin(3a) = tan (2a)
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  3. #3
    Newbie Coren's Avatar
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    is the question \frac{{\cos3a}-{\cos7a}}{{sin7a}+{sin3a}} = {\tan2a}

    or

    {\cos3a}-{\frac{cos7a}{\sin7a}}+{\sin3a} = {\tan2a}?

    Your syntax is a little unclear.

    Either way you may find this indentity useful: {\sin3a} = {\sin (a + 2a)} this also applies for cos and tan.
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  4. #4
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    Quote Originally Posted by bahram View Post
    Hi guys
    could you please help me to prove cos3a-cos7a/sin7a+sin3a=tan2a
    \frac{\cos(3a) - \cos(7a)}{\sin(7a) + \sin(3a)} =

    \frac{\cos(5a - 2a) - \cos(5a + 2a)}{\sin(5a + 2a) + \sin(5a - 2a)} =

    \frac{\cos(5a)\cos(2a) + \sin(5a)\sin(2a) - [\cos(5a)\cos(2a) - \sin(5a)\sin(2a)]}{\sin(5a)\cos(2a) + \cos(5a)\sin(2a) + \sin(5a)\cos(2a) - \cos(5a)\sin(2a)} =

    \frac{2\sin(5a)\sin(2a)}{2\sin(5a)\cos(2a)} =

    \frac{\sin(2a)}{\cos(2a)} = \tan(2a)
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  5. #5
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    hi

    thanks skeeter. it's the best one
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