Question

How do you simplify `cos(x)/(1-sin(x) - tan(x)?`?

Answer 1

Since `tan(x)=sin(x)/cos(x)`, we have that

`\frac{cos(x)}{1-sin(x)-tan(x)} = \frac{cos(x)}{1-sin(x)-sin(x)/cos(x)}`

Multiply numerator and denominator by `cos(x)`:

`\frac{cos^2(x)}{cos(x)-cos(x)sin(x)-sin(x)}`

But honestly, from this point I see no further semplifications, and neither wolframalpha goes any further. So, either the exercise is solved, or you miscopied it from your book maybe?