Question

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

Answer 1

Correct Answer - 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)`