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Prove that:
To Prove: cos-1 (4x3 – 3x) = 3 cos-1 x
Formula Used: cos 3A = 4 cos3 A – 3 cos A
Proof:
LHS = cos-1 (4x3 – 3x) … (1)
Let x = cos A … (2)
Substituting (2) in (1),
LHS = cos-1 (4 cos3 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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