SSC CGL 2021 PYQ — Question 67

The correct answer is option 1 i.e.  2 + $\sqrt{3}$.

⇒ 2cos² $\theta$ - 5 cos $\theta$ + 2 = 0

⇒ 2cos² $\theta$ - 4 cos $\theta$ - cos$\theta$ + 2 = 0

⇒ 2cos$\theta$(cos$\theta$ - 2) -1(cos$\theta$ - 2) = 0

⇒ (cos$\theta$ - 2)(2cos$\theta$ - 1)

⇒ cos$\theta$ = 1/2 and 2

cos$\theta$ cannot be beyond 1 so 2 is not possible.

cos$\theta$ = cos60

$\theta$ = 60.

= Now sec60 + tan60

= 2 + $\sqrt{3}$.