How do you verify #sinx/cosx + cosx/sinx = 1#?
You can't verify it since it is not an identity.
You can't since this is not true.
To prove that this is not an identity, find one
For example, you can take
As you know,
#sin(pi/3) / cos(pi/3) + cos(pi/3)/sin(pi/3) = (sqrt(3)/2)/(1/2) + (1/2)/(sqrt(3)/2) = sqrt(3)/1 + 1 / sqrt(3) = 4 / sqrt(3) != 1 #
Thus, this equation is not an identity.
The given equation is not true
and therefore can not be verified.
As an obvious counter-example