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Math Help - Double Angle Question

  1. #1
    Junior Member
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    Double Angle Question

    Show that sin S - sin T = 2.cos (S + T / 2) .sin (S - T / 2)

    (By the way, am I right in saying that you are not allowed to expand the RHS when the question asks to 'show'?)

    Thanks !
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  2. #2
    MHF Contributor
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    Hi

    You are allowed to expand the RHS using the usual trig identities cos(a+b) and sin(a-b)
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  3. #3
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    I still don't know how to do it.
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  4. #4
    MHF Contributor
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    On the right side

    \cos \left(\frac{S}{2}+\frac{T}{2}\right) = \cos \frac{S}{2} \cos \frac{T}{2} - \sin \frac{S}{2} \sin \frac{T}{2}

    \sin \left(\frac{S}{2}-\frac{T}{2}\right) = \sin \frac{S}{2} \cos \frac{T}{2} - \cos \frac{S}{2} \sin \frac{T}{2}

    Multiply both to get the RHS


    On the left side

    \sin S - \sin T = 2 \sin \frac{S}{2} \cos \frac{S}{2} - 2 \sin \frac{T}{2} \cos \frac{T}{2}
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