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We will learn how to prove the property of the inverse trigonometric function 3 arcsin(x) = arcsin(3x - 4x3) or, 3 sinβ1 x = sinβ1 (3x - 4x3)
Proof:
Let, sinβ1 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 = sinβ1 (3x - 4x3)
β 3 sinβ1 x = sinβ1 (3x - 4x3)
or, 3 arcsin(x) = arcsin(3x - 4x3) Proved
β Inverse Trigonometric Functions
11 and 12 Grade Math
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