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The expression (tan A)/(1-cotA)+(cot A)/...

The expression `(tan A)/(1-cotA)+(cot A)/(1-tan A)` can be written as

A

`sinA cos A+1`

B

`sec A coses A+1`

C

`tanA+cot A`

D

`sec A+cosec A`

Text Solution

Verified by Experts

The correct Answer is:
B
`(tanA)/(1-cotA)+(cotA)/(1-tanA)`
`=(sin^(2)A)/(cos A(sinA-cosA))+(cos^(2)A)/(sinA(cosA-sinA))`
`=(sin^(3)A-cos^(3)A)/(sinA cos A (sinA-cosA))`
`=(1+sinA cosA)/(sinA cosA(sinA-cosA))`
`=(1+sinAcosA)/(sinA cos A)=sec A cosec A+1`
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