## Calculus 8th Edition

$\frac{sin(x+y)}{cosxcosy}=tanx+tany$
Need to prove the identity $\frac{sin(x+y)}{cosxcosy}=tanx+tany$ Let us solve left side of the given identity. $\frac{sin(x+y)}{cosxcosy}=\frac{sinxcosy+cosxsiny}{cosxcosy}$ $\frac{sin(x+y)}{cosxcosy}=\frac{sinx}{cosx}+\frac{siny}{cosy}$ Hence, $\frac{sin(x+y)}{cosxcosy}=tanx+tany$