Question

If $\cos \left(2{\sin }^{-1}x\right)=\frac{1}{9}$, the value of x which satify equation is $\pm \frac{a}{b}$. Find the value of $a+b$

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is D $5$

Given, $\cos \left(2{\sin }^{-1}x\right)=\frac{1}{9}$
Let, ${\sin }^{-1}x=\theta$.
Then, $\cos 2\theta =\frac{1}{9}$

$1-2{\sin }^2\theta =\frac{1}{9}$ or $1-2x^2=\frac{1}{9}$

$x^2=\frac{4}{9}$ or $x=\pm \frac{2}{3}$

$\therefore a+b=2+3=5$