In which case we divide a trigonometry equation by cos theta like I want to say that sometimes we divide both numerator and denominator by cos theta why??? Give me example

When proving trigonometric identities or solving trig problems that involve more than one function, it's common to divide through by a function, or even multiply through by a function, in order to make the equation solvable by having just one function of x. For example, when proving that sec^2(x) = 1 + tan^2(x), one way is to divide the equation sin^2(x) + cos^2(x) = 1 by cos^2(x), and then simplify. Therefore, it is obvious that in some situations division is correct.