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The values of a for which the equation s...

The values of a for which the equation `sqrtasinx-2cosx=sqrt2+sqrt(2-a)` has solutions are

A

`p gt 0`

B

`p le 3`

C

`1 le p le 2`

D

`sqrt(5)-1 le p le 2`

Text Solution

Verified by Experts

The correct Answer is:
D
We must have `0 le p le 2`
Also `sqrt(2)+sqrt(2-p)le sqrt(p + 4)`
`rArr 2sqrt(4-2p)le 2p`
`rArr 4-2p le p^(2)`
`rArr p^(2)+2p-4le 0`
`rArr p in [sqrt(5)-1,2]`
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