If \(\frac{\cos \beta}{\sec \alpha}\) = 15 and \(\frac{\sin \beta}{\sec \alpha}\) = 16, then the value of sin²β is ___________.

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 14 Jul 2023 Shift 3)

Answer 1

Given

\(\frac{\cos \beta}{\sec \alpha}\) = 15

\(\frac{\sin \beta}{\sec \alpha}\) = 16

Calculation

Sec α = cos β/15 ......(1)

sin β = 16 × Sec α .....(2)

Putting the value of eq (1) in eq (2)

⇒ sin β = 16 × cos β/15

⇒ sin β/cos β = 16/15

⇒ P/B = 16/15

sin2β = P²/H²

H² = P² + B²

H2 = 256 + 225

H2 = 481

sin2β = 256/481

The value is 256/481.

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