Question

proove it with complete explanation​

Answer 1

Answer:

$L.H.S \\\\=\sqrt{\frac{secA - 1}{secA + 1} } +\sqrt{\frac{secA + 1}{secA - 1} }\\\\=\sqrt{\frac{(secA - 1)(secA-1)}{(secA + 1)(secA-1)} } + \sqrt{\frac{(secA + 1)(secA+1)}{(secA + 1)(secA-1)} }\\\\=\sqrt{\frac{(secA - 1)^{2}}{sec^{2}A - 1 } } + \sqrt{\frac{(secA + 1)^{2}}{sec^{2}A - 1 } }\\\\=\sqrt{\frac{(secA - 1)^{2}}{tan^{2} A } } + \sqrt{\frac{(secA + 1)^{2}}{tan^{2} A } }\\\\=\frac{secA - 1}{tanA} +\frac{secA + 1}{tanA} \\\\= \frac{2secA}{tanA} \\\\= \frac{2}{cosA} \frac{cosA}{sinA}$

$=\frac{2}{sinA} \\\\=2cosecA\\\\=R.H.S$