Prove that:√1+cos A/√1-cosA= cosecA+cotA.The question is from t

1.	Prove that:√1+cos A/√1-cosA= cosecA+cotA.The question is from trigonometric identities from class 10.
Answer» GIVEN $\sf : \implies \sqrt{ \dfrac{1 + cosA}{1 - cosA} } = cosecA + cotA$ To Prove $\sf : \implies \: cosecA + cotA$ Now Take $\sf : \implies \sqrt{ \dfrac{1 + cosA}{1 - cosA} }$ Rationalize The Denominator $\sf : \implies \sqrt{ \dfrac{1 + cosA}{1 - cosA} \times \dfrac{1 + cosA}{1 + cosA} }$ $\sf : \implies \: \sqrt{ \dfrac{(1 + cosA)^{2} }{(1 - cos ^{2}A) } }$ We Know that $\sf : \implies \: sin {}^{2} x + cos {}^{2} x = 1$ $: \implies \sf \: sin^{2} x = 1 - cos {}^{2} x$ Put the VALUE $\sf : \implies \sqrt{ \dfrac{(1 + cosA) {}^{2} }{sin^{2} A} }$ $\sf : \implies \dfrac{1 + cosA}{sinA}$ $\sf : \implies \: \dfrac{1}{sinA} + \dfrac{cosA}{sinA}$ $\sf : \implies \: cosecA + cotA$ HENCE Proved