Question

((sinx)/(1-cosx))+((1-cosx)/sinx)

Answer 1

looks like just a matter of simple addition

Answer 2

\(\bf \cfrac{sin(x)}{1-cos(x)}+\cfrac{1-cos(x)}{sin(x)}\implies \cfrac{sin^2(x)+[1-cos(x)][1-cos(x)]}{[1-cos(x)]sin(x)}\\ \quad \\
\cfrac{sin^2(x)+[1-cos(x)]^2}{[1-cos(x)]sin(x)}\\ \quad \\
\textit{expand the numerator, keeping in mind that }{\color{blue}{ sin^2(\theta)+cos^2(\theta)=1}}\)