Question

find the value of x?send full explanation please​

Answer 1

Step-by-step explanation:

We have,

$\cos(2 \sin^{ - 1} (x) ) = \frac{1}{9}$

$\implies1 - 2 \sin ^{2} ( \sin ^{ - 1} (x) ) = \frac{1}{9}$

$\implies2 \sin ^{2} ( \sin ^{ - 1} (x) ) = 1 - \frac{1}{9}$

$\implies2 x^{2} = \frac{8}{9}$

$\implies \: x^{2} = \frac{4}{9}$

$\implies \: x = ±\frac{2}{3}$