Answer
The identity is verified.
$\frac{1}{tan~θ~csc~θ}=cos~θ$
Work Step by Step
$csc~θ=\frac{1}{sin~θ}$
$tan~θ=\frac{sin~θ}{cos~θ}$
$\frac{1}{tan~θ~csc~θ}=\frac{1}{\frac{sin~θ}{cos~θ}~\frac{1}{sin~θ}}=\frac{1}{\frac{1}{cos~θ}}=1~\frac{cos~θ}{1}=cos~θ$
