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Verify the Identity
(sin m +sin n)/ (cos m + cos n) = tan(m + n/2)

  • Trig -

    I suspect you mean

    tan((m + n)/2)

    on the RHS

  • Trig -

    yes i do.

  • Trig -

    Use Lemma
    sin m + sin n = 2sin(m+n/2)cos(m-n/2)
    cos m + cos n = 2cos(m+n/2)cos(m-n/2)
    We get
    (sin m +sin n)/cos m + cos n) = sin(m+n/2)/cos(m+n/2) = tan m+n/2)

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