Question

3sin-1x=sin-1(3x-4x3),x€(-1/2,1/2) prove that ?​

Answer 1

Please see the attachment

Answer 2

$3sin^{-1}x=sin^{-1}(3x-4x^3)$, proved.

Step-by-step explanation:

Prove that, $3sin^{-1}x=sin^{-1}(3x-4x^3)$

Put $sin^{-1}x=\theta$

∴ $x =\sin \theta$

⇒ $\theta=\sin^{-1}x$                    .....(1)

We know that,

$\sin 3\theta=3\sin \theta-4\sin^3 \theta$

⇒ $\sin 3\theta=3x-4x^{3}$

⇒ $3\theta=\sin^{-1} (3x-4x^{3})$   ......(2)

From (1) and (2), we get

$3sin^{-1}x=sin^{-1}(3x-4x^3)$, proved.

Hence, $3sin^{-1}x=sin^{-1}(3x-4x^3)$, proved.