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If the inequality sin^2x+acosx+a^2>1+cos...

If the inequality `sin^2x+acosx+a^2>1+cosx` holds for any `x in R ,` then the largest negative integral value of a is `-4` (b) 3 (c) `-2` (d) `-1`

A

-4

B

-3

C

-2

D

-1

Text Solution

Verified by Experts

The correct Answer is:
B
`sin^2x+acosx+a^2gt1cosx`
Putting x = 0, we have
`a+a^2gt2`
`ora^2+a-2gt0`
`or (a+2)(a-1)gt0`
`or alt-2oragt1`
Therefore, the largest negative integral value of a is -3.
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