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Math Help - Prove that 3

  1. #1
    Junior Member
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    Prove that 3

    if sintheta = nsin(theta + 2 alpha)
    prove that tan(theta + alpha) = (1+n)/(1-n) *tan theta
    my incomplete soln -
    sin theta/ sin(theta+ 2 alpha) = n
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  2. #2
    Senior Member BAdhi's Avatar
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    I guess you've made some mistake here...

    I think what we have to prove is that  \tan (\theta +\alpha) = \frac{(1+n)}{(1-n)}\tan \alpha

    if so, take  \frac{(1+n)}{(1-n)}

    for this you'll need the following equation,
    \sin C +\sin D = 2\sin{\frac{(C+D)}{2}}.\cos{\frac{(C-D)}{2}}

    eventually you'll get,
     \frac{(1+n)}{(1-n)}=\frac{\tan{(\theta +\alpha)}}{\tan{\alpha}}
    Last edited by BAdhi; June 5th 2011 at 05:58 AM. Reason: replaced "simplify" to "take"
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  3. #3
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    sin(theta)/sin(theta+2alpha)=n/1
    sin(theta+2alpha) + sin(theta) / sin(theta+2alpha) - sin(theta) = 1+n/1-n
    using sin P + sin Q = 2sin[(P+Q)/2] cos[(P-Q)/2] and sin p - sin Q = 2cos[(P+Q)/2] sin[(P-Q)/2]
    we get tan(theta + alpha)/tan( alpha) = 1+n/1-n and hence required result
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