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If 0 lt alpha lt pi/2, then sqrt(2cotal...

If `0 lt alpha lt pi/2`, then `sqrt(2cotalpha+1/(sin^2alpha))` is equal to

A

`1+cotalpha`

B

`-1-cotalpha`

C

`1-cotalpha`

D

`-1+cotalpha`

Text Solution

Verified by Experts

The correct Answer is:
B
`sqrt(2cotalpha+1/sin^2alpha)=sqrt(2cot alpha+cosec^2alpha)`
`=sqrt(2cotalpha+1+cot^2alpha)`
`=abs(1+cotalpha)=-1-cotalpha`
[Since `aotalphalt-1" when "3pi//4ltalphaltpi`]
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