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