The set of values of 'a' for which the equation
`sqrt(a) "cos" x -2 "sin" x = sqrt(2) + sqrt(2-a)` has a solution is

Options

A. `(0, 2)`
B. `[0, 2]`
C. `(sqrt(5)-1, 2)`
D. `[sqrt(5)-1, 2]`

Answer

D

Explanation

The given equation will have a solution if
`a ge 0, 2 -a ge 0 " and " |sqrt(2) + sqrt(2-a)| le sqrt(a+4)`
`rArr a in [0, 2] " and " (sqrt(2) + sqrt(2-a)^(2)) le a + 4`
`rArr a in [0, 2] " and " a^(2) + 2a - 4 ge 0`
`rArr a in [0, 2] " and " a in (-oo, -sqrt(5)-1] cup [sqrt(5)-1, oo)`
`rArr a in [sqrt(5)-1, 2]`