We will learn how to prove the property of the inverse trigonometric function 3 arcsin(x) = arcsin(3x - 4x3) or, 3 sin−1 x = sin−1 (3x - 4x3)
Proof:
Let, sin−1 x = θ
Therefore, sin θ = x
Now we know that, sin 3θ = 3 sin θ - 4 sin3 θ
⇒ sin 3θ = 3x - 4x3
Therefore, 3θ = sin−1 (3x - 4x3)
⇒ 3 sin−1 x = sin−1 (3x - 4x3)
or, 3 arcsin(x) = arcsin(3x - 4x3) Proved
● Inverse Trigonometric Functions
11 and 12 Grade Math
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