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If 3 ^{ -1 }{ x } + ^{ -1 }{ x } = , then x=.....

Question

If $3 cos^{- 1} x + sin^{- 1} x = π$ , then $x = .....$

\frac{3}{2}

- \frac{1}{2}

\frac{1}{2}

\frac{1}{2}

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3 cos^{- 1} x + sin^{- 1} x = π

, then

x = .....

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Text solutionVerified

sin^{- 1} x + cos^{- 1} x = \frac{π}{2}

3 cos^{- 1} x + sin^{- 1} x = 2 cos^{- 1} x + cos^{- 1} x + sin^{- 1} x = π

\Rightarrow 2 cos^{- 1} x + \frac{π}{2} = π

\Rightarrow 2 cos^{- 1} x = \frac{π}{2}

cos^{- 1} x = \frac{π}{4}

x = cos (\frac{π}{4}) = \frac{1}{2}

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