We will learn how to prove the property of the inverse trigonometric function 3 arcsin(x) = arcsin(3x  4x\(^{3}\)) or, 3 sin\(^{1}\) x = sin\(^{1}\) (3x  4x\(^{3}\))
Proof:
Let, sin\(^{1}\) x = θ
Therefore, sin θ = x
Now we know that, sin 3θ = 3 sin θ  4 sin\(^{3}\) θ
⇒ sin 3θ = 3x  4x\(^{3}\)
Therefore, 3θ = sin\(^{1}\) (3x  4x\(^{3}\))
⇒ 3 sin\(^{1}\) x = sin\(^{1}\) (3x  4x\(^{3}\))
or, 3 arcsin(x) = arcsin(3x  4x\(^{3}\)) Proved
11 and 12 Grade Math
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