#### Answer

The required solution is False.

#### Work Step by Step

The given statement shows that in order to verify the identity $\frac{\sin x}{1+\cos x}=\frac{1-\cos x}{\sin x}$ , we need to multiply both sides with sin x (1+cosx) -- that is, the least common denominator. This is not true because in order to verify the identity, converting it into the sines and cosines form will be preferable.
Thus, the conversion into sine and cosines will help to identify the verified term more easily as they provide the more common basis for conversion.