Question

How would you write this equation in terms of sin and cos as well as simplify it from there?

Answer 1

Try this option:
$(1+ \frac{cosx}{sinx})(1- \frac{cosx}{sinx})- \frac{1}{sin^2x}= \frac{sin^2x-cos^2x}{sin^2x}- \frac{1}{sin^2x}=$
$= \frac{sin^2x-cos^2x-sin^2x-cos^2x}{sin^2x}=- \frac{2cos^2x}{sin^2x}.$
or -2ctg²x