SSC CHSL 2023 PYQ — Question 62

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

In triangle ABC, ∠A = 90°, ∠C = 45°

⇒ ∠B = 45° (since sum of angles in triangle = 180°)

Let the sides opposite 45° angles be 1 unit each, then hypotenuse = √2

So, for ∠C = 45°:

sec C = hypotenuse / adjacent = √2 / 1 = √2

sin C = opposite / hypotenuse = 1 / √2

Now:
sec C + sin C × sec C = √2 + (1/√2)(√2) = √2 + 1