Answer
$\frac{sin(x+y)}{cosxcosy}=tanx+tany$
Work Step by Step
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, $\frac{sin(x+y)}{cosxcosy}=tanx+tany$
