How do you show that (costheta)(sectheta) = 1(cosθ)(secθ)=1 if theta=pi/4θ=π4?

1 Answer
Feb 3, 2015

Let's look at the triangle:
enter image source here
We'll use angleAA in stead of thetaθ because of the picture.

Now cosA=b//hcosA=b/h and secA=h//bsecA=h/b by definition.

So their product is:

cosA*secA=b/h *h/b =1cosAsecA=bhhb=1 for all values of AA

If we come closer to A=pi/4A=π4 the value of
cosA->0cosA0 while the value of secA->oosecA

As long as AA is a little bit smaller than pi/4π4 then cosA*secAcosAsecA still come to 11. We can get as close as we want, the answer is still 11.

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