If xtan60° + cos45° = sec45°, then the value of x2 + 1 is?

Answer: Option B

$$\begin{array}{rl}& \Rightarrow x\tan 60^{\circ }+\cos 45^{\circ }=\sec 45^{\circ }\\ & \Rightarrow x.\sqrt{3}+\frac{1}{\sqrt{2}}=\sqrt{2}\\ & \Rightarrow x\sqrt{6}+1=2\\ & \Rightarrow x=\frac{1}{\sqrt{6}}\end{array}$$
Squaring both sides and addition 1 both sides
$$\begin{array}{rl}& \Rightarrow x^2+1={\left(\frac{1}{\sqrt{6}}\right)}^2+1\\ & \Rightarrow x^2+1=\frac{1}{6}+1\\ & \Rightarrow x^2+1=\frac{7}{6}\end{array}$$