[tex] \huge\boxed{♧ \: \mathfrak{ \underline{Answer} \: ♧}}[/tex]
here's the solution,
=》
[tex]f( \theta) = \cos( \theta) + 2 \cos( \frac{ \theta}{2} ) [/tex]
=》
[tex]f(60) = \cos(60) + 2 \cos( \frac{60}{2} ) [/tex]
=》
[tex]f(60) = \dfrac{1}{2} + 2 \cos(30) [/tex]
=》
[tex]f(60) = \dfrac{1}{2} + (2 \times \frac{ \sqrt{3} }{2})[/tex]
=》
[tex]f(60) = \dfrac{1}{2} + \sqrt{3} [/tex]
=》
[tex]f(60) = \dfrac{1 + 2 \sqrt{3} }{2} [/tex]
hence, correct option is C.