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Math Help - proving an addition identity????

  1. #1
    Senior Member
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    Question proving an addition identity????

    Using high school geometry only, show
    that sin(A+B) = sinAcosB + sinBcosA


    how would i show how one side equals the other side??
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  2. #2
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    consider



    in this figure, we have that NOPR is a rectangle, ON was extended and we get the point M. Join M and P and extend NR, point Q borns. Finally make QP orthogonal to MP and join M and Q.

    let \measuredangle\,OMP=\alpha and \measuredangle\,QMP=\beta. It's easy to prove that \measuredangle\,OMP=\measuredangle\,PQR=\alpha.

    compute \sin(\alpha+\beta) and we have it's equal to \frac{{\overline {QN} }}{{\overline {QM} }} = \frac{{\overline {QR}  + \overline {RN} }}{{\overline {QM} }} = \frac{{\overline {QR} }}{{\overline {QM} }} + \frac{{\overline {OP} }}{{\overline {QM} }}. Multiply the first quotient top and bottom by \overline{QP} and in the same fashion for the second quotient by \overline{MP} and you'll get the identity.
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