Question

Show that
sin(x)/1-cos(x) = 1+cos(x)/sin(x)

where x is any real numbered angle that is not an integer mulitple of pi.

Answer 1

start with your left hand side. Multiply by (1+cos(x)/(1+cos(x))

Answer 2

bottom turns into sin^2(x)

Answer 3

cancel a sin(x) from top and bottom.

Answer 4

\[\frac{\sin x}{1-\cos x}\times\frac{1+\cos x}{1+\cos x}=\frac{\sin x(1+\cos x)}{1-\cos ^2x}=\frac{\sin x(1+\cos x)}{\sin ^2x}\]

Answer 5

\[\frac{1+\cos x}{\sin x}\]