A) \[[-2,3]\]
B) \[[-2,1]\]
C) \[[2,4]\]
D) \[[1,5]\]
Correct Answer: C
Solution :
\[3-\cos \theta +\cos \left( \theta +\frac{\pi }{3} \right)\] \[=3-\cos \theta +\cos \theta .cos\frac{\pi }{3}-\sin \theta .\sin \frac{\pi }{3}\] \[=3-\cos \theta +\frac{1}{2}\cos \theta -\frac{\sqrt{3}}{2}\sin \theta \] \[=3-\frac{1}{2}\cos \theta -\frac{\sqrt{3}}{2}\sin \theta \] \[=3-\left[ \sin \frac{\pi }{6}\cos \theta +\cos \frac{\pi }{6}\sin \theta \right]\] \[=3-\sin \left( \theta +\frac{\pi }{6} \right)\] \[\sin ce-1\le \sin \left( \theta +\frac{\pi }{6} \right)\le 1\] The value of expression lies in [2, 4].
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