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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 sin1 x = sin1 (3x - 4x3)

Proof:  

Let, sin1 x = θ      

Therefore, sin θ = x

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

⇒ sin 3θ = 3x - 4x3

Therefore, 3θ = sin1 (3x - 4x3)

⇒ 3 sin1 x = sin1 (3x - 4x3)

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

 Inverse Trigonometric Functions






11 and 12 Grade Math

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