Prove that:
To Prove: sin-1 (3x – 4x3) = 3 sin-1 x
Formula Used: sin 3A = 3 sin A – 4 sin3 A
Proof:
LHS = sin-1 (3x – 4x3) … (1)
Let x = sin A … (2)
Substituting (2) in (1),
LHS = sin-1 (3 sin A – 4 sin3 A)
= sin-1 (sin 3A)
= 3A
From (2), A = sin-1 x,
3A = 3 sin-1 x
= RHS
Therefore, LHS = RHS
Hence proved.