Question

prove that : secA/SecA+1 + secA/SecA-1=2cosec²A

Answer 1

hope it may help you

Answer 2

$\frac{seca}{seca - 1} + \frac{seca}{seca + 1} \\ \\ = seca( \frac{seca + 1 + seca - 1}{ {sec}^{2}a - 1 } ) \\ \\ = seca( \frac{2seca}{ {tan}^{2} a} ) \\ \\ = \frac{2 {sec}^{2} a}{ {tan}^{2} a}$

$= 2. \frac{1}{ {cos}^{2} a} . \frac{ {cos}^{2} a}{ {sin}^{2} a} \\ \\ = \frac{2}{ {sin}^{2} a} \\ \\ = 2 {cosec}^{2} a$