# 3 arcsin(x) = arcsin(3x - 4x$$^{3}$$)

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

Inverse Trigonometric Functions