SSC CHSL 2024 PYQ — Question 59

The correct answer is option 3 i.e. $2-\sqrt3$.

${sin\ 60°- cos\ 60°}\over {sin\ 60°+cos\ 60°}$

⇒ $\frac{\frac{\sqrt3}{2}-\frac{1}{2}}{\frac{\sqrt3}{2}+\frac{1}{2}}$

⇒($\sqrt3$ - 1)/ ($\sqrt3$ + 1)

Multiplying the numerator and denominator by $\sqrt3$ + 1,

⇒( $\sqrt3$ - 1)²/ (3 - 1)

⇒( 3 + 1 -2$\sqrt3$)/2

⇒$2-\sqrt3$