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

1 Answer
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)#.