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If ^{ -1 }{ x } = ^{ -1 }{ x } then

Question

If $sin^{- 1} x = cot^{- 1} x$ then

x^{2} = \frac{5 - 1}{2}

x^{2} = \frac{5 + 1}{2}

x = \frac{5 + 1}{2}

x = \frac{5 - 1}{2}

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Daniel Discussed

sin^{- 1} x = cot^{- 1} x

then

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Text solutionVerified

sin^{- 1} x = cot^{- 1} x

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

\Rightarrow x = \frac{1}{1 + x ^{2}} \Rightarrow x^{2} = \frac{1}{1 + x ^{2}}

x^{2} + x^{4} - 1 = 0 \Rightarrow x^{4} + x^{2} - 1 = 0

\Rightarrow x^{2} = \frac{- 1 \pm 1 + 4}{2} ∴ x^{2} = \frac{5 - 1}{2}

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