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In [-pi, pi], solution of inequality………....

In `[-pi, pi]`, solution of inequality………. `cos 2x+5cos x +3 ge 0` is

A

`[-pi, pi]`

B

`[(-5pi)/(6), (pi)/(6)]`

C

`[0, pi]`

D

`[(-2pi)/(3), (2pi)/(3)]`

Text Solution

Verified by Experts

The correct Answer is:
D
In `[-pi, pi]`, solution ………….
`cos 2x +5 cos x + 3ge 0 2cos^(2)x +5cos x + 2ge 0`
`(cos x +2)(2cos x +1)ge 0 implies 2cos x + 1 ge 0`
`(cos x + 2 ge 0)`
`cos x ge - (1)/(2) implies x epsilon [- (2pi)/(3), (2pi)/(3)]`
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