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If the equation k sin x + sqrt(k-2)cos x...

If the equation `k sin x + sqrt(k-2)cos x+(tan alpha+cot alpha)=0, 0 lt alpha lt(pi)/(2)`, possesses real solution, then k belongs to

A

`(-oo,-3]uu[2,oo)`

B

`[-3,2]`

C

`[0,2)`

D

R

Text Solution

Verified by Experts

The correct Answer is:
A
For real solution `sqrt(k^(2)+k-2)ge|tan alpha + cot alpha| ge 2`
`rArr k^(2)+k-6 ge 0`
`rArr k in (-oo, -3] uu[2,oo)`
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