The value of sin265° + sin225° + cos235° + cos255° is?

Answer: Option C

$$\begin{array}{rl}& \Rightarrow {\sin }^{2}65^{\circ }+{\sin }^{2}25^{\circ }+{\cos }^{2}35^{\circ }+{\cos }^{2}55^{\circ }\\ & \Rightarrow {\sin }^{2}65^{\circ }+{\sin }^2\left({90}^{\circ }-{65}^{\circ }\right)+\left[{\cos }^2{35}^{\circ }+{\cos }^2\left({90}^{\circ }-{35}^{\circ }\right)\right]\\ & \Rightarrow \left({\sin }^2{65}^{\circ }+{\cos }^2{65}^{\circ }\right)+\left({\cos }^2{35}^{\circ }+si{n}^2{35}^{\circ }\right)\\ & \Rightarrow 1+1\\ & \Rightarrow 2\end{array}$$