Question

kindly solve this...​

Answer 1

Step-by-step explanation:

To prove,

$\boxed{\sqrt{\dfrac{1+cosA}{1-cosA}} = cosecA + cotA}$

Solving LHS:

$\sf \bf :\longmapsto \sqrt{\dfrac{1+cosA}{1-cosA}}$

Rationalizing,

$\sf \bf :\longmapsto \sqrt{\dfrac{1+cosA}{1-cosA}\times \dfrac{1+cosA}{1+cosA}}$

$\sf \bf :\longmapsto \sqrt{\dfrac{(1+cosA)^2}{1^2 - cos^2A}}$

$\sf \bf :\longmapsto \sqrt{\dfrac{(1+cosA)^2}{sin^2A}}$

$\sf \bf :\longmapsto \dfrac{1+cosA}{sinA}$

Seperating the terms

$\sf \bf :\longmapsto \dfrac{1}{sinA} + \dfrac{cosA}{sinA}$

$\sf \bf :\longmapsto cosecA + cotA$

= LHS

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