What is the period of $\tan x \cot x?$ I was given this question today. What I did was simplify the expression , and it reduced to a constant function. So it had no fundamental period.
But my teacher told me that the answer was $\frac{\pi}{2}$. How is it so?
Best Answer
$$f(x) = \dfrac{\tan x}{\tan x}\neq 1$$ $$f(x) = 1, x\neq k\dfrac{\pi}{2}, k\in\mathbb{I}\\$$
The period is $\pi / 2$, since the function isn't defined for integral multiple of pi/2. So as egreg also mentions, it will have holes in graph.
For a function to be periodic, it must have translational symmetry in its graph.