How do you find the exact expression of cos (pi / 2) - sec (-pi/2)?

1 Answer
KillerBunny
Oct 31, 2015

You can't write that expression because it would lead to a division by zero.

Explanation:

First of all, use the fact that, by definition, sec(x)=1/cos(x).

So, your expression becomes

cos(pi/2) - 1/cos(-pi/2)

Now you can use the fact that cos(-x)=cos(x), and it becomes

cos(pi/2) - 1/cos(pi/2)

Now, the problem is that cos(pi/2)=0, and so the first term is zero, but the second would be something like 1/0 which is obviously impossible to write. So, your expression can't be evaluated in that point, because -pi/2 is out of the domain of sec(x).

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