Calculus Problem

Question

Differentiate 

Option:

1. -1
2. -2csc(x)sec(x)
3. 2csc(x)sec(x)
4. 

Answer 1

Do you mean y = (1 + sin(x)) / (1 - cos(x))

Use the quotient rule: d/dx (u/v) = (v*u' - u*v') / v²

So, y' = { (1 - cos(x)) * cos(x) - (1 + sin(x)) * sin(x) } / (1 - cos(x))²

Simplify the top: cos(x) - cos²(x) - sin(x) - sin²(x) = cos(x) - sin(x) - 1

(cos(x) - sin(x) - 1) / (1 - cos(x))²