SSC CGL 2024 PYQ — Question 74

The correct answer is option 2 i.e.  ${α\ \over \sqrt{1 - α^2}}$.

Given that, sin31° = $\alpha$

⇒ sin (90° - 59°) = $\alpha$

⇒ cos59° = $\alpha$

cos x = $B \over H$

⇒ B = $\alpha$ and H = 1

Using Pythagoras theorem, P² = H² - B²

⇒ P² = 1 - $\alpha^2$

⇒ P = $\sqrt​{1 - \alpha^2} ​$

Also, cot x = $B \over P$

Now, cot59° = $\alpha \over {\sqrt{1 - \alpha^2}}$

Hence the required answer is $\alpha \over {\sqrt{1 - \alpha^2}}$.