Question

How do you prove `(cos^2x + tan^2x ) / (cos^2x + sin^2x )-1= 0`?

Answer 1

I'm afraid you can't as the statement is not actually true, at least for all values of `x`.

Explanation:

Here is a graph of the function:

graph{((tan(x))^2+(cos(x))^2)/((sin(x))^2+(cos(x))^2)-1 [-9.4,9.4, -5.4, 16.02]}

As you can see the function is not necessarily equal to 0 always. So the statement cannot be proved as it is false.