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Math Help - Prove identities, can anyone help?

  1. #1
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    Red face Prove identities, can anyone help?

    Hi, I am working through proving some trigonomic identities and need some help on the following, can someone please help?

    cos3x - cos7x = tan2x
    sin7x + sin3x

    I know I need to end up with: sin2x = tan2x
    cos2x

    Need some help getting there?

    Thanks for any help.
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by joemc22 View Post
    Hi, I am working through proving some trigonomic identities and need some help on the following, can someone please help?

    cos3x - cos7x = tan2x
    sin7x + sin3x

    I know I need to end up with: sin2x = tan2x
    cos2x

    Need some help getting there?

    Thanks for any help.
    Use these formulae :

    \sin a+\sin b=2 \sin \tfrac{a+b}{2} \cos \tfrac{a-b}{2}
    \sin a-\sin b=2 \cos \tfrac{a+b}{2} \sin \tfrac{a-b}{2}
    \cos a+\cos b=2 \cos \tfrac{a+b}{2} \cos \tfrac{a-b}{2}
    \cos a-\cos b=-2 \sin \tfrac{a+b}{2} \sin \tfrac{a-b}{2}

    (They directly come from the addition & subtraction formulae of cos and sin)
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  3. #3
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    Prove identities

    Thanks, but
    Not sure what to do with that, I'm working from a list of basic identities and need to know the next steps, haven't seen that formulae before?
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  4. #4
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    Trig Identity

    Hello joemc22

    As Moo said, use the formulae :

    \sin a+\sin b=2 \sin \tfrac{a+b}{2} \cos \tfrac{a-b}{2}

    \cos a-\cos b=-2 \sin \tfrac{a+b}{2} \sin \tfrac{a-b}{2}

    \frac{\cos 3x - \cos 7x}{\sin 7x + \sin 3x} = \frac{-2 \sin \tfrac{3x+7x}{2} \sin \tfrac{3x - 7x}{2}}{2 \sin \tfrac{7x+3x}{2}\cos\tfrac{7x-3x}{2}}

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

    = \frac{\sin 2x}{\cos 2x}

    =\tan 2x

    Grandad
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