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Prove that:
To Prove: cos-1 (2x2 - 1) = 2 cos-1 x
Formula Used: cos 2A = 2 cos2 A – 1
Proof:
LHS = cos-1 (2x2 - 1) … (1)
Let x = cos A … (2)
Substituting (2) in (1),
LHS = cos-1 (2 cos2 A – 1)
= cos-1 (cos 2A)
= 2A
From (2), A = cos-1 x,
2A = 2 cos-1 x
= RHS
Therefore, LHS = RHS
Hence proved.
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