Q. 94.2( 8 Votes )

Prove that : 3 sin–1x = sin–1 (3x – 4x3), x .[CBSE 2018]

Answer :

To Prove: 3 sin–1x = sin–1 (3x – 4x3)

Proof: 

we know that,

sin3θ = 3 sinθ - 4 sin3θ.....(1)

Let sinθ = x, then

θ = sin-1 x

Put the value in equation 1, we get,

sin3θ = 3x - 4x3

3θ = sin-1(3x - 4x3)

3 sin–1x = sin–1 (3x – 4x3)

Hence, Proved.

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