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For all values of theta,3-costheta+cos(t...

For all values `of theta,3-costheta+cos(theta+(pi)/(3))` lie in the interval

A

`-2,3`

B

`-2,1`

C

`2,4`

D

`1,5`

Text Solution

Verified by Experts

The correct Answer is:
C
`3-costheta+cos(theta+(pi)/(3))`
`=3-costheta+(1)/(2)"cos"theta-(sqrt(3))/(2)sintheta`
`=3-(1)/(2)"cos"theta-(sqrt(3))/(2)sintheta`
`=3-"sin"(pi)/(6)"cos "theta-"cos"(pi)/(6)"sin "theta=3-sin(theta+(pi)/(6))`
Since , `-1lesinthetale1`
`therefore-1le-sin(theta+(pi)/(6))le1`
`rArr-1+3le3-sin(theta+(pi)/(6))le1+3`
`rArr2le3-sin(theta+(pi)/(6))le4`
Hence , the value of expression lies in [2,4].
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