Question

prove that √cosecA+1/cosecA-1 -√ cosecA-1/cosec A+1= 2 tan A​

Answer 1

Answer:

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Answer 2

$\huge\mathbb{QUESTION \mapsto: }$

⚛⚛⚛⚛prove that √cosecA+1/cosecA-1 -√ cosecA-1/cosec A+1= 2 tan A☯☯☯☯☯☯☯☯✅

using formula===========>

$\sf\ 1 + {cot}^{2} \theta = {cosec}^{2} \theta \\ \\ \sf\ \implies: \boxed{ \sf{cot}^{2} \theta} = {cosec}^{2} \theta - 1$

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$\huge\mathbb{SOLUTION\mapsto: }$

$\sf\ \frac{ \sqrt{cosec \theta + 1}}{ \sqrt{cosec \theta - 1} } - \frac{ \sqrt{cosec \theta - 1} }{ \sqrt{cosec \theta + 1} } \\ \\ \bf\ \implies: \frac{({ \sqrt{cosec \theta + 1}})({ \sqrt{cosec \theta + 1}}) - ({ \sqrt{cosec \theta - 1} })({ \sqrt{cosec \theta - 1} })}{ { \sqrt{cosec \theta - 1} } \times { \sqrt{cosec \theta + 1}} } \\ \\ \bf\ \implies: \frac{(cosec \theta + 1) - (cosec \theta - 1)}{ \sqrt{ {cosec}^{2} \theta - {1}^{2} } } \\ \\ \bf\ \implies: \frac{ \cancel{cosec \theta }+ 1 \cancel{ - cosec \theta} + 1 }{ \sqrt{ {cosec}^{2} \theta - 1} } \\ \\ \bf\ \implies: \frac{2}{ \sqrt{ {cot}^{2} \theta } } \\ \\ \bf\ \implies: \frac{{2}}{cot \theta} \\ \\ \bf\ \implies:{2 \times \frac{1}{cot \theta}} \\ \\ \bf\boxed{ \sf\underline{ \implies:2tan \theta \: \: \: \ddot \smile}}$