The value of co s^260^ + 4 se c^230^ - ta n^245^ ^230^ + co s^230^ is?

Answer: Option B

$$\begin{array}{rl}& \frac{\text{co}{\text{s}}^2{60}^{\circ }+4\text{se}{\text{c}}^2{30}^{\circ }-\text{ta}{\text{n}}^2{45}^{\circ }}{{\sin }^2{30}^{\circ }+\text{co}{\text{s}}^2{30}^{\circ }}\\ & \Rightarrow \frac{{\left(\frac{1}{2}\right)}^2+4{\left(\frac{2}{\sqrt{3}}\right)}^2-1}{1}\\ & \left({\sin }^2\text{A}+{\cos }^2\text{A}=\text{1}\right)\\ & \Rightarrow \frac{1}{4}+\frac{4\times 4}{3}-1\\ & \Rightarrow \frac{1}{4}+\frac{16}{3}-1\\ & \Rightarrow \frac{3+64-12}{12}\\ & \Rightarrow \frac{55}{12}\end{array}$$