PROVE THAT : sin(a+b)/cos a cos b = tan a tan b

First use... sin(a+b) = sinacosb + sinbcosa .... then it is

(sinacosb + sinbcosa)/(cosacosb) = (sinacosb)/(cosacosb) + (sinbcosa)/(cosacosb) ... now simplify and get

sina/cosa + sinb/cosb = tana + tanb OK!

[sin(a+b)]/[cos(a)cos(b)] = tan(a)tan(b)

Simplifying LHS:

[sin(a)cos(b) + cos(a)sin(b)]/cos(a)cos(b)

= sin(a)/cos(a) + sin(b)/cos(b)

= tan(a) + tan(b)

Are you sure the RHS isn't tan(a) + tan(b)?

Vahucel really provided you with
the best solution.
sorry, I opted for the wrong directed thumb:
i;e; down, whereas i wanted to rated thumb up !

:-(

PS: it's late in the night in France: 1:45am.