# How do you verify the identity: sin(A+B) = (tanA+tanB)/(secA secB)?

$R N = \sin \frac{A}{\cos} A + \sin \frac{B}{\cos} B = \frac{\sin A . \cos B + \sin B . \cos A}{\cos A . \cos B}$
$R D = \frac{1}{\cos} A \left(\frac{1}{\cos} B\right) = \frac{1}{\cos A . \cos B}$
$\frac{R N}{R D} = \left(\sin A . \cos B + \sin B . \cos A\right) = \sin \left(A + B\right)$ Correct.