Question

How do you prove `costhetacottheta=costheta`?

Answer 1

The identity is not true in general

Explanation:

Consider `theta = pi/3`. Then `cos(theta) = 1/2`, and `cot(theta) = cos(theta)/sin(theta) = (1/2)/(sqrt(3)/2) =sqrt(3)/3`

So `cos(theta)cot(theta) = 1/2(sqrt(3)/3) = sqrt(3)/6 != 1/2 = cos(theta)`