Question

How do you simplify the expression `cos^2x/(1+sinx)`?

Answer 1

`1-sin x`

Explanation:

`cos^2x/(1+sinx) = (1-sin^2 x)/(1+sinx) = ((1-sin x)(1+sin x))/(1+sin x)`

Now we proceed to cancell `(1+sin x)` in both numerator and denominator because they configure a so called avoidable discontinuity. So

`cos^2x/(1+sinx) = 1-sin x`