SSC CGL 2023 PYQ — Question 67

The correct answer is option 1  i.e. $\frac{256}{481}$.

Given that

If $\frac{cos ⁡β}{secα}$ = 15 and $\frac{sin⁡β}{sec⁡α}$ = 16,

cos β = 15 sec α ......(1

sin β = 16 sec α .......(2

Equation 2 ÷ Equation 1

tan β = 16/15 = Perpendicular (P)/Base (B)

As we know,

Hypotanous (H) = √(P² + B²)

⇒ H = √(16² + 15²) = √(256 + 225) = √481

⇒ H² = 481

Hence, the value of sin²β = P²/H² = 256/481