Question 1004983
it's actually easier to solve than you might think.


first recognize that 1 is equivalent to sin^2(x) + cos^2(x).


also recognize that tan^2(x) = sin^2(x) / cos^2(x).


you can either multiply numerator and denominator of the expression on the left by cos^2(x), or you can divide numerator and denominator of the expression on the right by cos^2(x).


working on the left:


your numerator of (tan^2(x) + 1) * cos^2(x) becomes:


tan^2(x) * cos^2(x) + 1 * cos^2(x) which becomes:


sin^2(x) + cos^2(x).


similarly, your denominator becomes sin^2(x) - cos^2(x).


working on the right:


your numerator of 1 becomes sin^2(x) + cos^(x).


(sin^2(x) + cos^2(x)) / cos^2(x) becomes:


sin^2(x) / cos^2(x) + cos^2(x) / cos^2(x) which becomes:


tan^2(x) + 1


similarly, your denominator becomes tan^2(x) - 1.


you are correct that tan^2(x) + 1 = sec^2(x), but that didn't really help you here, as far as i can tell.