I understand that, to prove that a trig equation is NOT an identity, we must find at least one angle to plug into the equation such that, one side of the equation does not equal the other side.
I also understand that we have to keep plugging in values until we find one that works.
Here is my question:
If I always choose pi/4 (an angle in quad 1), 3pi/4 (an angle in quad 2), 5pi/4 (an angle in quad 3), and 7pi/4 (an angle in quad 4), am I always guaranteed that one of those angle will work simply because I chose one angle in each quadrant?