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If 3π/4<α<π, then sqrt(2cotalpha+1/(sin...

If 3π/4<α<π, 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

`sqrt(2cotalpha+1/sin^2alpha)`
`=sqrt(2cotalpha+cosec^2alpha)`
`=sqrt(2cotalpha+cot^2alpha+1)`
`=sqrt((1+cotalpha)^2)`
`=|1+cotalpha|`
As `(3pi)/4 lt alpha lt pi`, `cotalpha` will be negative.
`:.|1+cotalpha| = -1-cot alpha`
So, optopon -`(b)` is the correct option.
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