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Prove that : (tanA)/(1-cotA)+(cotA)/(1-...

Prove that : `(tanA)/(1-cotA)+(cotA)/(1-tanA)=1+secA".cosec"A`

A

`sinAcosA+1`

B

`secA.cosecA+1`

C

`tanA+cotA`

D

`secA+cosecA`

Text Solution

Verified by Experts

The correct Answer is:
B
`tanA/(1-cotA)+cotA/(1-tanA)=tan^2A/(tanA-1)+1/(tanA-tan^2A)`
`=1/(tanA-1)[tan^2A-1/tanA]`
`(tan^3A-1)/((tanA-1).tanA)`
`=(tan^2+tanA+1)/tanA`
`=tanA+cotA+1`
`=secA.cosecA+1`
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