Solve: ( ^ -1 x )=1 6 - Vidyadip

Question

Solve: $\cos\big(\sin^{-1}\text{x}\big)=\frac{1}{6}$

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Answer

$\cos\big(\sin^{-1}\text{x}\big)=\frac{1}{6}$
$\Rightarrow\cos\Big(\cos^{-1}\sqrt{1-\text{x}^2}\Big)=\frac{1}{6}$
$\Rightarrow\sqrt{1-\text{x}^2}=\frac{1}{6}$
$\Rightarrow1-\text{x}^2=\frac{1}{36}$
$\Rightarrow1-\frac{1}{36}=\text{x}^2$
$\Rightarrow\text{x}^2=\frac{35}{36}$
$\Rightarrow\text{x}=\pm\frac{\sqrt{35}}{6}$

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