Question

How do you show that `(costheta)(sectheta) = 1` if `theta=pi/4`?

Answer 1

Let's look at the triangle:

We'll use `angleA` in stead of `theta` because of the picture.

Now `cosA=b//h` and `secA=h//b` by definition.

So their product is:

`cosA*secA=b/h *h/b =1` for all values of `A`

If we come closer to `A=pi/4` the value of
`cosA->0` while the value of `secA->oo`

As long as `A` is a little bit smaller than `pi/4` then `cosA*secA` still come to `1`. We can get as close as we want, the answer is still `1`.

Summary
`lim_(A->pi//4) cosA*secA=1`