# Appendix D - Trigonometry - D Exercises - Page A32: 56

$\frac{sin(x+y)}{cosxcosy}=tanx+tany$

#### 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, $\frac{sin(x+y)}{cosxcosy}=tanx+tany$

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