Question

sinx/1+cosx + 1+cosx/sinx

Answer 1

\[\frac{\sin(x)}{1+\cos(x)}+\frac{1+\cos(x)}{\sin(x)}\] \[\frac{\sin^2x+1+2\cos(x)+\cos^2x}{(1+\cos(x)~~~)\sin(x)}\]
\[\frac{1+2\cos(x)+\cos^2x+\sin^2x}{(1+\cos(x)~~~)\sin(x)}\]
\[\frac{1+2\cos(x)+1}{(1+\cos(x)~~~)\sin(x)}\]
\[\frac{2+2\cos(x)}{(1+\cos(x)~~~)\sin(x)}\]\[\frac{2+2\cos(x)}{\sin(x)+\cos(x)\sin(x)}\]

Answer 2

Is it OK to factor out the 2 in the numerator in the second to last step, and then cancel out the 1+cos(x) in the numerator and denominator? Which would give us 2/sin(x) as the last step.