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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`

Text Solution

Verified by Experts

`sqrt(2cotalpha +1/sin^2alpha) = sqrt(2cotalpha+cosec^2alpha)`
`=sqrt(2cotalpha+1+cot^2alpha)`
`=sqrt((1+cotalpha)^2)`
`=1+cotalpha.`
So, option `(b)` is the correct option.
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