If cos2 sin -1 x -1-9- then x -A- Only 2-3B- 2-3- -2-3C- N either 2-3 nor -2-3D- Only -2-3

The correct option is B 2/3, 2/3cos(2sin^ 1x)=1/9 ⇒ cos(sin^ 12x√(1 x^2))=1/9 ⇒ cos(cos^ 1√(1 4x^2+4x^4))=1/9 ⇒ 1 2x^2=1/9⇒ 2x^2=1 1/9=8/9 ⇒ x^2=4/9⇒ x=±2/3. ...

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Byju's Answer

Standard XII

Mathematics

Basic Inverse Trigonometric Functions

If cos2 sin -...

Question

If $c o s (2 s i n^{- 1} x) = \frac{1}{9}$ , then x=

O n l y \frac{2}{3}

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O n l y \frac{- 2}{3}

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\frac{2}{3}, \frac{- 2}{3}

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N e i t h e r \frac{2}{3} n o r \frac{- 2}{3}

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Solution

The correct option is C $\frac{2}{3}, \frac{- 2}{3}$
$c o s (2 s i n^{- 1} x) = \frac{1}{9}$
$\Rightarrow c o s (s i n^{- 1} 2 x \sqrt{1 - x^{2}}) = \frac{1}{9}$
$\Rightarrow c o s (c o s^{- 1} \sqrt{1 - 4 x^{2} + 4 x^{4}}) = \frac{1}{9}$
$\Rightarrow 1 - 2 x^{2} = \frac{1}{9} \Rightarrow 2 x^{2} = 1 - \frac{1}{9} = \frac{8}{9}$
$\Rightarrow x^{2} = \frac{4}{9} \Rightarrow x = \pm \frac{2}{3}$ .

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