Trigonometry

Prove that
cos(A+B)cosC - cos(B+C)cosA = sinBsin(C-A)

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  1. LS
    = (cosAcosB - sinAsinB)cosC - (cosBcosC- sinBsinC)(cosA)
    = cosAcosBcosC - sinAsinBcosC - cosAcosBcosC + cosAsinBsinC
    = cosAsinBsinC - sinAsinBcosc

    RS = sinB(sinCcosA - cosCsinA)
    = cosAsinBsinC -sinAsinBcosC
    = LS

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