Question

Prove it plz for me?
1+sinθ/1-sinθ = cosecθ+1/cosecθ-1
plz solve it in detail!

Answer 1

Answer on Question#37594 - Math - Trigonometry

$$1 + \frac{\sin \theta}{1 - \sin \theta} = \cosec \theta + \frac{1}{\cosec \theta - 1}$$

Solution.

$$\cosec \theta = \frac{1}{\sin \theta}.$$

We obtain

$$1 + \frac{\sin \theta}{1 - \sin \theta} = \frac{1}{\sin \theta} + \frac{1}{\frac{1}{\sin \theta} - 1};$$ $$1 + \frac{\sin \theta}{1 - \sin \theta} = \frac{1}{\sin \theta} + \frac{\sin \theta}{1 - \sin \theta};$$ $$1 = \frac{1}{\sin \theta}$$ $$\sin \theta = 1 \rightarrow$$ $$\theta = \frac{\pi}{2} + 2\pi n, \text{ where } n \in \mathbb{Z}.$$