Answer
When we sketch the graph of these two functions, we can see that the graphs are the same.
This is an identity:
$tan(\frac{\pi}{2}-\theta) = cot~\theta$
Work Step by Step
$y = tan(\frac{\pi}{2}-\theta)$
$y = cot~\theta$
When we sketch the graph of these two functions, we can see that the graphs are the same.
We can use the following identities:
$sin~(-a) = -sin~a$
$cos~(-b) = cos~b$
We can demonstrate the identity:
$tan(\frac{\pi}{2}-\theta) = \frac{sin(\frac{\pi}{2}-\theta)}{cos(\frac{\pi}{2}-\theta)}$
$tan(\frac{\pi}{2}-\theta) = \frac{-sin(\theta-\frac{\pi}{2})}{cos(\theta-\frac{\pi}{2})}$
$tan(\frac{\pi}{2}-\theta) = \frac{cos~\theta}{sin~\theta}$
$tan(\frac{\pi}{2}-\theta) = cot~\theta$
This is an identity:
$tan(\frac{\pi}{2}-\theta) = cot~\theta$
