Find the counterexample to shows that the equation sec (alpha) - cos (alpha) = sin (alpha) sec (alpha) is not an identity.

Question

Please explain.

Answer 1

there are many counterexamples. For instance,

sec(pi/4) - cos(pi/4) = √2 - 1/√2
sin(pi/4)*sec(pi/4) = 1/√2 * √2 = 1

not equal. In fact, for any alpha not a multiple of pi, they are not equal.