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If the inequality sin^(2) x+a cos x+a^(2...

If the inequality `sin^(2) x+a cos x+a^(2) gt 1+ cos x` holds for any `x in R`, then the largest negative integral value of a is

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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