In this problem, it is easier to start from the RHS. We need to perform a trick.

We multiply numerator and denominator of the fraction by the conjugate of the denominator. (We saw this idea in the sections Rationalizing the Denominator (in surds) and in dividing complex numbers.)

This will give us an expression in the denominator that we can simplify, using sin2 θ + cos2 θ = 1.

`"RHS" = (sin x)/(1-cos x)`

`=(sin x)/(1 - cos x)xx (1 + cos x)/(1 + cos x)`

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

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

`=(1 + cos x)/(sin x)`

`="LHS"`

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