MCQ
The minimum value of $\cos \,2\theta \, + \,\cos \,\theta $ for real values $\theta $ is
  • $-9/8$
  • B
    $0$
  • C
    $-2$
  • D
    none of these 

Answer

Correct option: A.
$-9/8$
a
Let $S=\cos 2 \theta+\cos \theta$

$=2 \cos ^{2} \theta-1+\cos \theta$

$=-1+2\left(\cos ^{2} \theta+\frac{1}{2} \cos \theta+\frac{1}{16}\right)-\frac{1}{8}$

$=-\frac{9}{8}+2\left(\cos \theta+\frac{1}{4}\right)^{2} \geq-\frac{9}{8}$

So, the minimum value $S=-9 / 8$

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