Simplify: $$\frac{\sin \theta}{1-\cos\theta}$$​​

The expression to simplify: $$\frac{\sin \theta}{1-\cos\theta}$$

multiplying by $$\frac{1+cos\theta}{1+cos\theta}$$​​

​$$=\frac{\sin \theta}{1-\cos\theta}\times\frac{1+cos\theta}{1+cos\theta} \\ \ \\ =\frac{sin\theta(1+cos\theta)}{(1-cos\theta)(1+cos\theta)}\\ \ \\ =\frac{sin\theta(1+cos\theta)}{\sin^2\theta}\\ \ \\ =\frac{(1+cos\theta)}{\sin\theta}\\ \ \\ =\frac{1}{\sin\theta}+\frac{\cos\theta}{\sin\theta}\\ \ \\ =\cosec\theta + \cot\theta$$

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