SSC CHSL 2024 PYQ — Question 57

The correct answer is option 3 i.e. $\frac{7}{5}$.

Given, 3tanθ = 4

⇒ tanθ = 4/3  (= P/B)

Let the perpendicular P be 4x and base, B be 3x.

So, hypotenuse will be 5x. (3, 4, 5 is Pythagorian triplet)

Now, sinθ = P/H = 4x/5x = 4/5

And cosθ = B/H = 3x/5x = 3/5

Given expression, (9sinθ + 2cosθ)/(9sinθ − 2cosθ)

⇒ (9 × 4/5 + 2 × 3/5)/(9 × 4/5 - 2 × 3/5)

⇒ 42/30 = 7/5