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Question Number 211321 by efronzo1 last updated on 06/Sep/24

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Answered by som(math1967) last updated on 06/Sep/24

$$\frac{1+sin\theta }{cos\theta }=p$$$$\Rightarrow \frac{{(1+sin\theta )}^2}{{cos}^2\theta }=p^2$$$$\Rightarrow \frac{{(1+sin\theta )}^2}{(1+sin\theta )(1-sin\theta )}=p^2$$$$\Rightarrow \frac{1+sin\theta }{1-sin\theta }=p^2$$$$\Rightarrow \frac{1+\frac{1}{\mathrm{cosec}\theta }}{1-\frac{1}{\mathrm{cosec}\theta }}=p^2$$$$\therefore \frac{\mathrm{cosec}\theta +1}{\mathrm{cosec}\theta -1}=p^2$$

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