Question

Prove that each equation is not a trigonometric identity by producing a counterexample.
I will type

Answer 1

\[\sec ^{2}x-1=\frac{\cos x}{\csc x}\]

Answer 2

Try a few different values for x and find one which does not satisfy the equation; e.g.,
\[x = \pi/2, \ \pi/3, \ \pi/6, \ \pi/4\]
At least one of these does not satisfy the equation.