Question

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

Answer 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)