A) Greater than \[-\frac{3}{2}\]
B) Less than or equal to \[\frac{3}{2}\]
C) Greater than or equal to \[-\frac{3}{2}\] and less than or equal to 3
D) None of these
Correct Answer: C
Solution :
We have \[\cos 2\theta +2\cos \theta =2{{\cos }^{2}}\theta -1+2\cos \theta \] \[=2{{\left( \cos \theta +\frac{1}{2} \right)}^{2}}-\frac{3}{2}\] Now \[2{{\left( \cos \theta +\frac{1}{2} \right)}^{2}}\ge 0\]for all \[\theta \] \[\therefore \,\,2{{\left( \cos \theta +\frac{1}{2} \right)}^{2}}-\frac{3}{2}\ge \frac{-3}{2}\]for all \[\theta \]. Þ \[\cos 2\theta +2\cos \theta \ge \frac{-3}{2}\]for all \[\theta \]
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