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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

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