Given 3tanAtanB=1,show that 2cos(A+B)=cos(A-B) ?

1 Answer
Jun 12, 2017

Given

3tanAtanB=1

1tanAtanB=3

cosAcosBsinAsinB=31

By componendo and dividendo

cosAcosB+sinAsinBcosAcosBsinAsinB=3+131

cos(AB)cos(A+B)=42=2

2cos(A+B)=cos(AB)

Proved