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

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Answer 1 · 2015-02-03T00:26:10

Let's look at the triangle:
enter image source here
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#