\(tan(x) + tan(y) = \frac{sin(x + y)}{cos(x)cos(y)}\)
\(\frac{sin(x)}{cos(x)} + \frac{sin(y)}{cos(y)} = \frac{sin(x + y)}{cos(x)cos(y)}\)
\(\frac{sin(x)cos(y)}{cos(x)cos(y)} + \frac{sin(y)cos(x)}{cos(x)cos(y)} = \frac{sin(x + y)}{cos(x)cos(y)}\)
\(\frac{sin(x)cos(y) + sin(y)cos(x)}{cos(x)cos(y)} = \frac{sin(x + y)}{cos(x)cos(y)}\)
\(\frac{sin(x + y)}{cos(x)cos(y)} = \frac{sin(x + y)}{cos(x)cos(y)}\)
