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

Solution(By Examveda Team)

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