3 arcsin(x) = arcsin(3x - 4x3)

We will learn how to prove the property of the inverse trigonometric function 3 arcsin(x) = arcsin(3x - 4x3) or, 3 sinβˆ’1 x = sinβˆ’1 (3x - 4x3)

Proof:  

Let, sinβˆ’1 x = ΞΈ      

Therefore, sin ΞΈ = x

Now we know that, sin 3ΞΈ = 3 sin ΞΈ - 4 sin3 ΞΈ

β‡’ sin 3ΞΈ = 3x - 4x3

Therefore, 3ΞΈ = sinβˆ’1 (3x - 4x3)

β‡’ 3 sinβˆ’1 x = sinβˆ’1 (3x - 4x3)

or, 3 arcsin(x) = arcsin(3x - 4x3)           Proved

● Inverse Trigonometric Functions






11 and 12 Grade Math

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