A) Only 2/3
B) Only -2/3
C) 2/3, -2/3
D) Neither 2/3 nor -2/3
Correct Answer: C
Solution :
\[\cos (2{{\sin }^{-1}}x)=\frac{1}{9}\] \[\Rightarrow \cos ({{\sin }^{-1}}2x\sqrt{1-{{x}^{2}}})=\frac{1}{9}\] Þ\[\cos ({{\cos }^{-1}}\sqrt{1-4{{x}^{2}}+4{{x}^{4}}})=\frac{1}{9}\] Þ \[1-2{{x}^{2}}=\frac{1}{9}\Rightarrow 2{{x}^{2}}=1-\frac{1}{9}=\frac{8}{9}\] Þ \[{{x}^{2}}=\frac{4}{9}\Rightarrow x=\pm \frac{2}{3}\].
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