SSC CGL 2025 PYQ — Question 59

The correct answer is option 2 i.e. $-\frac{5}{12}$.

$\sin A = \frac{5}{13}$

⇒ $\sin^2 A = \frac{25}{169}$

In the 2nd quadrant, cos A is negative.

$\sin^2 A + \cos^2 A = 1$

⇒ $\frac{25}{169} + \cos^2 A = 1$

⇒ $\cos^2 A = 1 - \frac{25}{169} = \frac{144}{169}$

⇒ $\cos A = -\sqrt{\frac{144}{169}} = -\frac{12}{13}$

⇒ $\sec A = \frac{1}{\cos A} = \frac{1}{-12/13} = -\frac{13}{12}$

⇒ $\sin A \times \sec A = \frac{5}{13} \times \left( -\frac{13}{12} \right) = -\frac{5}{12}$