Solve: `Cos(Sin^-1x)=1/6` - Mathematics

Question

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

Solution

$\cos (\sin^{- 1} x) = \frac{1}{6}$

⇒ $\cos (\cos^{- 1} \sqrt{1 - x^{2}}) = \frac{1}{6}$

⇒ $\sqrt{1 - x^{2}} = \frac{1}{6}$

⇒ $1 - x^{2} = \frac{1}{36}$

⇒ $1 - \frac{1}{36} = x^{2}$

⇒ $x^{2} = \frac{35}{36}$

⇒ $x = \pm \frac{\sqrt{35}}{6}$

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Inverse Trigonometric Functions (Simplification and Examples)

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Q 3 Q 2.4 Q 1.1

Chapter 4: Inverse Trigonometric Functions - Exercise 4.08 [Page 54]

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RD Sharma Mathematics [English] Class 12

Chapter 4 Inverse Trigonometric Functions
Exercise 4.08 | Q 3 | Page 54

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Solve: $Cos ({Sin}^{- 1} x) = \frac{1}{6}$ - Mathematics

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