The equation `"sin"^(4) x - (k +2)"sin"^(2) x - (k + 3) = 0` possesses a solution, if

Options

A. `k gt -3`
B. `k lt -2`
C. `-3 le k le -2`
D. `k in Z`

Answer

C

Explanation

We have,
`"sin"^(4) x -(k + 2)"sin"^(2)x - (k +3) = 0`
`rArr "sin"^(2) x = ((k+2) +- sqrt((k+2)^(2) + 4(k+3)))/(2)`
`rArr "sin"^(2)x = ((k+2)+-(k+4))/(2)`
`rArr "sin"^(2) x = k + 3, -1`
`rArr "sin"^(2) x = k + 3`
The equation will have a solution, if
`0 le k + 3 le 1 rArr -3 le k le -2`