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[5costheta+3cos(theta+pi/3)+3] lies betw...

`[5costheta+3cos(theta+pi/3)+3]` lies between

A

`4` and `10`

B

`-4` and `10`

C

`-10` and `4`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
B
`3cos(theta+pi/3)=3{costhetacospi/3-sinthetasinpi/3}`
`=3costheta*1/2-3sinthetasqrt3/2`
`=3/2costheta-3sqrt3/2sintheta`
`5costheta+3cos(theta+pi/3)+3`
`=5costheta+3/2costheta=3sqrt3/2sintheta+3`
`=1/2(13costheta-3sqrt3sintheta)+3`
`=sqrt(169+27)/2*cos(theta+phi)+3`
`=sqrt196/2cos(theta+phi)+3`
...
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