If xsin60°.tan30° - tan²45° = cosec60°.cot30° - sec²45° then x = ?

Solution(By Examveda Team)

$${\text{ }}x\sin {60^ \circ }.\tan {30^ \circ } - \tan^2 {45^ \circ } = $$       $$\operatorname{cosec} {60^ \circ }.$$   $$\cot {30^ \circ } - $$   $${\sec ^2}{45^ \circ }$$
$$\eqalign{ & \Rightarrow x \times \frac{{\sqrt 3 }}{2} \times \frac{1}{{\sqrt 3 }} - 1 = \frac{2}{{\sqrt 3 }} \times \sqrt 3 - {\left( {\sqrt 2 } \right)^2} \cr & \Rightarrow \frac{x}{2} - 1 = 2 - 2 \cr & \Rightarrow \frac{x}{2} - 1 = 0 \cr & \Rightarrow \frac{x}{2} = 1 \cr & \Rightarrow x = 2 \cr} $$