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Prove that `sqrt((1+cosA)/(1-cosA))=("cosec"A+cotA).`

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Prove that `sqrt((1+cosA)/(1-cosA))=("cosec"A+cotA).`
A. `"cosec"A-cotA`
B. `"cosec"A+cotA`
C. `"cosec"AcotA`
D. none of these
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Correct Answer - B
`sqrt((1+cosA)/(1-cosA))=sqrt(((1+cosA))/((1-cosA))xx((1+cosA))/((1+cosA)))=((1+cosA))/(sqrt(1-cos^(2)A))=((1+cosA))/(sqrt(sin^(2)A))`
`=((1+cosA))/(sinA)=((1)/(sinA)+(cosA)/(sinA))=("cosec"A+cotA).`
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