Proving Trig Identities: Response

a) The equation tan(x)^2+cos(x)^2=sin(x)^2 is not a trig identity. We can verify that by putting it into the calculator, and looking at both how the graph of the rhs and lhs do not match up, and by looking at the table to see that the y1 and y2 columns don't match up.




















b) The equation 1-sec(x)^2=-tan(x)^2 is a trig identity. We can verify, but not prove this using the graph on our calculator.





















c) The reason that you can only use a calculator to verify a trig identity, and not prove it is because your calculator cannot do the algebra. While you can look at the graph to verify whether you have solved the identity, your calculator cannot show you the algebra in getting to the answer.