# How do you verify (sin z + cos z) (tan z + cot z) = sec z + csc z?

$\tan z + \cot z = \sin \frac{z}{\cos} z + \cos \frac{z}{\sin} z = \frac{{\sin}^{2} z + {\cos}^{2} z}{\sin z \cos z} = \frac{1}{\sin z \cos z}$. On the left of given equation, it reduces to (1/cos z +1/sin z)= sec z + csc z, as required..
${\sin}^{2} z + {\cos}^{2} z = 1$