MCQ
$\cos \,\,2\theta + 2\,\,\cos \theta $ is always
- AGreater than $ - \frac{3}{2}$
- BLess than or equal to $\frac{3}{2}$
- ✓Greater than or equal to $ - \frac{3}{2}$ and less than or equal to $3$
- DNone of these
$ = 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 $.
==> $\cos 2\theta + 2\cos \theta \ge \frac{{ - 3}}{2}$ for all $\theta $
Also max. value of this expression is $3.$
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