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We will learn how to prove the property of the inverse trigonometric function 3 arccos(x) = arccos(4x3 - 3x) or, 3 cosβ1 x = cosβ1 (4x3 - 3x)
Proof:
Let, cosβ1 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 = cosβ1 (4x3 - 3x)
β 3 cosβ1 x = cosβ1 (4x3 - 3x)
or, 3 arccos(x) = arccos(4x3 - 3x). Proved.
β Inverse Trigonometric Functions
11 and 12 Grade Math
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