A) Only \[2/3\]
B) Only \[-2/3\]
C) \[2/3,-2/3\]
D) Neither \[2/3\] nor\[-2/3\]
Correct Answer: B
Solution :
\[\cos \,\left( 2{{\sin }^{-1}}x \right)=\frac{1}{9}\Rightarrow \cos \left( {{\sin }^{-1}}2x\sqrt{1-{{x}^{2}}} \right)=\frac{1}{9}\] \[\Rightarrow \,\,\cos \left( {{\cos }^{-1}}\sqrt{1-4{{x}^{2}}+4{{x}^{4}}} \right)=\frac{1}{9}\] \[\Rightarrow \,\,1-2{{x}^{2}}=\frac{1}{9}\Rightarrow 2{{x}^{2}}=1-\frac{1}{9}=\frac{8}{9}\Rightarrow {{x}^{2}}=\frac{4}{9}\] \[\Rightarrow \,\,x=\pm \frac{2}{3}\]
You need to login to perform this action.
You will be redirected in
3 sec
