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

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Answer 1 · 2016-02-14T03:29:38

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

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.

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