If sin31° = $$\frac{x}{y}{\text{,}}$$ then the value of sec31° - sin59° is?

A. $$\frac{{{x^2}}}{{y\sqrt {{y^2} + {x^2}} }}$$

B. $$\frac{{{x^2}}}{{y\sqrt {{y^2} - {x^2}} }}$$

C. $$ - \frac{{{y^2}}}{{\sqrt {{y^2} - {x^2}} }}$$

D. $$ - \frac{{{x^2}}}{{\sqrt {{y^2} - {x^2}} }}$$

Answer: Option B

Solution(By Examveda Team)

sin31° = $$\frac{x}{y}{\text{,}}$$
∴ sec31° - sin59°
$$\eqalign{ & = \frac{y}{{\sqrt {{y^2} - {x^2}} }} - \frac{{\sqrt {{y^2} - {x^2}} }}{y} \cr & = \frac{{{y^2} - ({y^2} - {x^2})}}{{y\sqrt {{y^2} - {x^2}} }} \cr & = \frac{{{x^2}}}{{y\sqrt {{y^2} - {x^2}} }} \cr} $$