SSC CGL 2023 PYQ — Question 52

The correct answer is option 3  i.e. √6 - √2.

cosec75° = cosec(45° + 30°)

Using the given relation,

$\frac{sec45^\circ×sec30^\circ×cosec45^\circ​​​​​​×cosec30^\circ}{sec45^\circ×cosec30^\circ+cosec45^\circ×sec30^\circ}$

⇒ $\frac{\sqrt{2}×{2\over \sqrt{3}}×\sqrt{2}×2}{\sqrt{2}×2+\sqrt{2}×{2\over \sqrt{3}}}$

⇒ ${8 \over \sqrt{3}} \over {2(\sqrt{6} + \sqrt{2}) \over \sqrt{3}}$

⇒ 4/(√6 + √2)

Rationalising the above expression,

⇒ 4(√6 - √2)/(6 - 2)

⇒ 4(√6 - √2)/4 = √6 - √2