Question

√secA+1÷√sexA-1=cotA+cosecA

Answer 1

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Answer 2

Solution-

The given expression is,

$=\frac{\sqrt{\sec A+1}}{\sqrt{\sec A-1}}\\ \\=\sqrt\frac{{\sec A+1}}{\sec A-1}}\\ \\=\sqrt\frac{(\sec A+1)(\sec A+1)}{(\sec A-1)(\sec A+1)}\\\\=\sqrt\frac{(\sec A+1)^2}{\sec^2 A-1}\\\\=\sqrt\frac{(\sec A+1)^2}{\tan^2 A}\\\\=\frac{(\sec A+1)}{\tan A}\\\\=\frac{\sec A}{\tan A}+\frac{1}{\tan A}\\\\=\frac{1}{\sin A}+\cot A\\\\=\csc A+\cot A\\\\=\cot A+\csc A\ \ (Proved)$