Answer
makes sense
Work Step by Step
This statement makes sense because $1-sin(x)\ne cos(x)$. We need to find the least common denominator for the subtraction:
$\displaystyle \frac{cos(x)}{1-sin(x)}-\frac{sin(x)}{cos(x)}=\frac{cos^2x-sin(x)+sin^2x}{(1-sin(x))cos(x)}=\frac{1-sin(x)}{(1-sin(x))cos(x)}=sec(x)$
provided $sin(x)\ne 1$
