SSC Selection Post 2022 PYQ — Question 73

The correct answer is option 4 i.e. 2.

cot C = cot θ = 3 = 3/1

Height (AB) = 1; Base (BC) = 3; Hypotenuse (AC) = √(1² + 3²) = √10

$cosC(sinC + sinA)\over{sinA(cosC-cosA)}$

$=\frac{\frac{3}{\sqrt{10}} \left(\frac{1}{\sqrt{10}} + \frac{3}{\sqrt{10}}\right)}{\frac{3}{\sqrt{10}} \left(\frac{3}{\sqrt{10}} - \frac{1}{\sqrt{10}}\right)}$

$= \frac{\frac{3}{\sqrt{10}} \times \frac{4}{\sqrt{10}}}{\frac{3}{\sqrt{10}} \times \frac{2}{\sqrt{10}}}$

= 2