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

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

Proof:  

Let, cosβˆ’1 x = ΞΈ      

Therefore, cos ΞΈ = x

Now we know that, sin 3ΞΈ = 4 cos3 ΞΈ - 3 cos ΞΈ

β‡’ cos 3ΞΈ = 4x3 - 3x

Therefore, 3ΞΈ = cosβˆ’1 (4x3 - 3x)

β‡’ 3 cosβˆ’1 x = cosβˆ’1 (4x3 - 3x)

or, 3 arccos(x) = arccos(4x3 - 3x).           Proved.

● Inverse Trigonometric Functions







11 and 12 Grade Math

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