Question

please give me its solution

Answer 1

$\cos \theta + \cos 2\theta = \cos \theta + 2 { \cos }^{2} \theta - 1 \\ = 2 { \cos }^{2} \theta + 2 \cos \theta - \cos \theta - 1 \\ = 2 \cos \theta( \cos \theta + 1) - ( \cos \theta + 1) \\ = (2 \cos \theta - 1)( \cos \theta + 1) \\ minimum \: \: value \: \: for \: \: this \: \: \\ expression \: \: corresponds \: \: to \: \: \\ minimum \: \: value \: \: for \: \: \cos \theta \:$

$minimum \: \: value \: \: for \: \: \cos \theta \: \: is \: \: - 1 \\ therefore \\ minimum \: \: value \: \: for \: \: given \\ expression \: \: is \: \: (2 \times - 1 - 1) \times ( - 1 + 1) \\ = 0 \\ option \: \: (c)$