trignometry

prove:
sin(a+b)/cosacosb=tana+tanb

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  1. sin(a+b)/cos(a)cos(b) =
    = (sin(a)cos(b)+cos(a)sin(b))/cos(a)cos(b)
    = sin(a)cos(b)/(cos(a)cos(b) +
    cos(a)sin(b)/(cos(a)cos(b)
    = sin(a)/cos(a) + sin(b)/cos(b)
    = tan(a) + tan(b)

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