Question

3sin^-1x = sin^-1(3x – 4x³), x ∈ [- \(\frac { 1 }{ 2 }\), \(\frac { 1 }{ 2 }\) ]

Answer 1

Let sin^-1 = θ
∴ sin θ = x
Also,
∴ sin 3θ = 2 sinθ – 4sin³θ = 3x – 4x³
∴ 3θ = sin^-1(3x – 4x³)
or 3 sin^-1x = sin^-1(3x – 4x³), x ∈ [- \(\frac { 1 }{ 2 }\), \(\frac { 1 }{ 2 }\) ]