question_answer

If \[\cos \theta =\frac{8}{17}\] and \[\theta \] lies in the 1st quadrant, then the value of \[\cos (30{}^\circ +\theta )+\cos (45{}^\circ -\theta )+\]\[\cos (120{}^\circ -\theta )\] is

A)  \[\frac{23}{17}\left( \frac{\sqrt{3}-1}{2}+\frac{1}{\sqrt{2}} \right)\]

B)  \[\frac{23}{17}\left( \frac{\sqrt{3}+1}{2}+\frac{1}{\sqrt{2}} \right)\]

C)  \[\frac{23}{17}\left( \frac{\sqrt{3}-1}{2}-\frac{1}{\sqrt{2}} \right)\]         

D)  \[\frac{23}{17}\left( \frac{\sqrt{3}+1}{2}-\frac{1}{\sqrt{2}} \right)\]

E)  None of these