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Math Help - grade 12 trig identities

  1. #1
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    grade 12 trig identities

    Hey everyone, just wondering if anyone can figure this identity out.

     \ sin4x - sin2x/sin2x = \cos3x/cosx

    I already worked with the left side and ended up with 2cos2x-1 by using the double angle formula -> sin2x=2sinxcosx
    Im stuck on what to do next.

    any help is appreciated, thanks in advance.
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  2. #2
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    Quote Originally Posted by aries View Post
    Hey everyone, just wondering if anyone can figure this identity out.

     \ sin4x - sin2x/sin2x = \cos3x/cosx

    I already worked with the left side and ended up with 2cos2x-1 by using the double angle formula -> sin2x=2sinxcosx
    Im stuck on what to do next.

    any help is appreciated, thanks in advance.
    Note that:


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

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


    LHS = 2 \cos(2x) - 1 = \cos(2x) + \cos(2x) - 1.


    Now do you see how to get from LHS to RHS?
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