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If (3pi)/4 lt alpha lt pi, then sqrt(2c...

If `(3pi)/4 lt alpha lt pi`, then `sqrt(2cotalpha+1/(sin^2alpha))` is equal to (a) `1-cotalpha` (b) `1+cotalpha` (c) `-1+cotalpha` (d) `-1-cotalpha`

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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