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

1 Answer
Feb 3, 2015

Let's look at the triangle:
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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