NDA 2025 · PYQ · Inverse trigonometric functions · medium
Let y = sin⁻¹(x − 4x³/27). What is y equal to?
- A.sin⁻¹ x
- B.sin⁻¹(x/3)
- C.3 sin⁻¹ x
- D.3 sin⁻¹(x/3)✓ Correct
Let x/3 = sinθ, so x = 3sinθ. Then x − 4x³/27 = 3sinθ − 4·27sin³θ/27 = 3sinθ − 4sin³θ = sin(3θ). Hence y = sin⁻¹(sin 3θ) = 3θ = 3 sin⁻¹(x/3).
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