SSC CGL 2024 PYQ — Question 52

The correct answer is option 2 i.e. 3.

$\bigg( {cosecA\over cosecA-1}+{cosecA\over cosecA+1} \bigg) \bigg( {secA\over secA-1}+{secA\over secA+1} \bigg)^{-1}$

$=\bigg( {cosec60^\circ\over cosec60^\circ-1}+{cosec60^\circ\over cosec60^\circ+1} \bigg) \bigg( {sec60^\circ\over sec60^\circ-1}+{sec60^\circ\over sec60^\circ+1} \bigg)^{-1}$

$=\bigg( {2/\sqrt3\over (2/\sqrt3)-1}+{2/\sqrt3\over (2/\sqrt3)+1} \bigg) \bigg( {2\over 2-1}+{2\over 2+1} \bigg)^{-1}$

$=\bigg( {2/\sqrt3\over (2-\sqrt3)/\sqrt3}+{2/\sqrt3\over (2+\sqrt3)/\sqrt3} \bigg) \bigg( {2}+{2\over 3} \bigg)^{-1}$

$=\bigg( {2\over 2-\sqrt3}+{2\over 2+\sqrt3} \bigg) \bigg({8\over 3} \bigg)^{-1}$

$=\bigg( {2(2+\sqrt3)\over (2-\sqrt3)(2+\sqrt3)}+{2(2-\sqrt3)\over (2+\sqrt3)(2-\sqrt3)} \bigg)\times \bigg({3\over 8} \bigg)$

= [(4 + 2√3) + (4 - 2√3)] × (3/8)

= 8 × (3/8)

= 3

Therefore, the correct answer is 3