If 2 ^230^ 1 - ^230^ + ^245^ - ^20^ = x 60^ , then the value of x is?

Answer: Option B

$$\begin{array}{rl}& \frac{2{\tan }^2{30}^{\circ }}{1-{\tan }^2{30}^{\circ }}+{\sec }^{2}45^{\circ }-{\sec }^2{0}^{\circ }=x\sec 60^{\circ }\\ & \Rightarrow \frac{2\times {\left(\frac{1}{\sqrt{3}}\right)}^2}{1-{\left(\frac{1}{\sqrt{3}}\right)}^2}+{\left(\sqrt{2}\right)}^2-1=x\times 2\\ & \Rightarrow \frac{2\times \frac{1}{3}}{1-\frac{1}{3}}+2-1=2x\\ & \Rightarrow \left(\frac{2}{3}\times \frac{3}{2}\right)+2-1=2x\\ & \Rightarrow 2=x\times 2\\ & \Rightarrow x=1\end{array}$$