# If $\theta$ lies in the first quadrant and $\cos\theta=\large\frac{8}{17}$,then the value of $\cos(30^{\large\circ}+\theta)+\cos(45^{\large\circ}-\theta)+\cos(120^{\large\circ}-\theta)$ ?

$\begin{array}{1 1}(A)\;\large\frac{23(\sqrt 3-\sqrt 2-1)}{34}&(B)\;\large\frac{23(\sqrt 3+\sqrt 2+1)}{34}\\(C)\;\large\frac{34(\sqrt 3-\sqrt 2-1)}{23}&(D)\;\large\frac{23(\sqrt 2-\sqrt 3-4)}{34}\end{array}$

• $\cos(a\pm b)=\cos a\cos b\mp \sin a.\sin b$