SSC CHSL 2024 PYQ — Question 68

The correct answer is Option 1 i.e. $\frac{23}{49}$.

Given that,

⇒ $\sin \theta = \frac{15}{17} = \frac{P}{H}$

By Pythagoras theorem

⇒ H² = B² + P²

here, P = Perpendicular, B = Base, and H = Hypotaneous

⇒ 17² = B² + 15²

⇒ 289 = B² + 225

⇒ B² = 64

⇒ B = 8

So, 

⇒ cotθ = B/P = 8/15

⇒ sinθ = 15/17

⇒ tanθ = P/B = 15/8

⇒ secθ = H/B = 17/8

Putting the values in the given equation

⇒ $\frac{15 \times \frac{8}{15} + 17 \times \frac{15}{17}}{8 \times \frac{15}{8} + 16 \times \frac{17}{8}}$

⇒ $\frac{8 + 15}{15 + 34}$ 

⇒ $\frac{23}{49}$