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in Trigonometry by (27.7k points)
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Prove that:

\(\sin^{-1}(3\mathrm x -4\mathrm x^3)=3\sin^{-1}\mathrm x, |\mathrm x|\leq\frac{1}{2}\)

1 Answer

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by (25.7k points)
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Best answer

To Prove: 

sin -1 (3x – 4x 3) = 3 sin -1

Formula Used: sin 3A = 3 sin A – 4 sin 3

Proof: 

LHS = sin -1 (3x – 4x 3) … (1) 

Let x = sin A … (2) 

Substituting (2) in (1), 

LHS = sin -1 (3 sin A – 4 sin 3 A) 

= sin -1 (sin 3A) 

= 3A 

From (2), A = sin -1 x, 

3A = 3 sin -1

= RHS 

Therefore, LHS = RHS 

Hence proved.

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