Prove that:
To Prove: cos-1 (1 – 2x2) = 2 sin-1 x
Formula Used: cos 2A = 1 – 2 sin2 A
Proof:
LHS = cos-1 (1 – 2x2) … (1)
Let x = sin A … (2)
Substituting (2) in (1),
LHS = cos-1 (1 – 2 sin2 A)
= cos-1 (cos 2A)
= 2A
From (2), A = sin-1 x,
2A = 2 sin-1 x
= RHS
Therefore, LHS = RHS
Hence proved.