Question

Prove the following: 3sin⁻¹x=sin⁻¹(3x-4x³),x⋲[-1/2,1/2]

Answer 1

Put x= sin Q

Q = sin inverse x - - - - - - - - 1

The equation becomes,

Sin inverse ( 3sinQ - 4 sin cube Q)

As 3sinQ - 4SincubeQ = Sin3Q then,

Sin inverse(sin3Q) = 3Q = 3sin inverse x(from 1)

Hope you get your answer.☺️

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