Answer :

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.


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