Prove that:

To Prove: cos^{-1} (4x^{3} – 3x) = 3 cos^{-1} x

Formula Used: cos 3A = 4 cos^{3} A – 3 cos A

Proof:

LHS = cos^{-1} (4x^{3} – 3x) … (1)

Let x = cos A … (2)

Substituting (2) in (1),

LHS = cos^{-1} (4 cos^{3} A – 3 cos A)

= cos^{-1} (cos 3A)

= 3A

From (2), A = cos^{-1} x,

3A = 3 cos^{-1} x

= RHS

Therefore, LHS = RHS

Hence proved.

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