Asked by Sarah Fuller
prove:
sin(a+b)/cosacosb=tana+tanb
sin(a+b)/cosacosb=tana+tanb
Answers
Answered by
FredR
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)
= (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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