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The solution set of (5+4 cos theta)(2 co...

The solution set of `(5+4 cos theta)(2 cos theta+1)=0` in the interval `[0,2 pi]` is

A

`{(pi)/(3),(2pi)/(3)}`

B

`{(pi)/(3),pi}`

C

`{(2pi)/(3),(4pi)/(3)}`

D

`{(2pi)/(3),(5pi)/(3)}`

Text Solution

Verified by Experts

The correct Answer is:
C
We have ,`(5+4costheta)(2costheta+1)=0`
`rArrcostheta=-(5)/(4)` which is not possible.
`therefore2costheta+1=0rArrcostheta=-(1)/(2)`
`rArrtheta=(2pi)/(3),(4pi)/(3)`
`therefore` Solution set is `{(2pi)/(3),(4pi)/(3)}in[0,2pi]`.
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