SSC CGL 2023 PYQ — Question 54

The correct answer is Option 2 i.e. $\frac{9}{2}$.

Given that

The value of sec²54° - cot²36° + $\frac{3}{2}$ sin²37° × sec²53° + $\frac{2}{\sqrt{3}}$tan60°

⇒  sec²54° - cot²36° + $\frac{3}{2}$ sin²37° × sec²53° + $\frac{2}{\sqrt{3}}$tan60°

⇒  sec²54° - cot²(90° - 54°) + $\frac{3}{2}$ sin²37° × sec²(90° - 37°) + $\frac{2}{\sqrt{3}}$ × $\sqrt{3}$

⇒  sec²54° - tan²54° + $\frac{3}{2}$ sin²37° × cosec²37° + 2

⇒ 1 + (3/2) + 2

⇒ (2 + 3 + 4)/2

⇒ 9/2