Question

Prove that : (√1+cosA/1-cosA) + (√1-cosA/1+cosA)= 2cosecA

Answer 1

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Answer 2

$\sqrt{ \frac{1 + cosA}{1 - cosA} } + \sqrt{ \frac{1 - cosA}{1 + cosA} } \\ \\ = \frac{ \sqrt{1 + cosA} }{ \sqrt{1 - cosA} } + \frac{ \sqrt{1 - cosA} }{ \sqrt{1 + cosA} } \\ \\ = \frac{1 + cosA + 1 - cosA}{ \sqrt{1 - {cos}^{2}A } } \\ \\ = \frac{2}{sinA} \\ \\ = 2cosecA$