ΔXYZ is right angled at Y. If m∠Z = 45°, then find the value of $$\left( {{\text{cosecX}} - \frac{2}{{\sqrt 3 }}} \right) = ?$$

A. $$\frac{{2 - \sqrt 3 }}{{2\sqrt 3 }}$$

B. $$\frac{{1 - \sqrt 6 }}{{\sqrt 2 }}$$

C. $$\frac{{\sqrt 6 - 2}}{{\sqrt 3 }}$$

D. $$ - \frac{1}{{\sqrt 3 }}$$

Answer: Option C

Solution (By Examveda Team)

$$\eqalign{ & {\text{cosec X}} - \frac{2}{{\sqrt 3 }} \cr & = \frac{{\sqrt 2 x}}{x} - \frac{2}{{\sqrt 3 }} \cr & = \sqrt 2 - \frac{2}{{\sqrt 3 }} \cr & = \frac{{\sqrt 6 - 2}}{{\sqrt 3 }} \cr} $$