If sin(sin−121+cos−1x)=1, then find the value of x.

We havesin(sin−121+cos−1x)=1⇒sin(sin−121+cos−1x)=sin2π⇒sin−121+cos−1x=2π⇒6π+cos−1x=2π∴cos−1x=3π∴x=cos3π=21

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If (^{-1}{1}{2}+^{-1}x)=1, then find the value of x.

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If $sin (sin^{- 1} \frac{1}{2} + cos^{- 1} x) = 1$ , then find the value of $x$ .

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Camila Discussed

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

, then find the value of

x

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12 mins ago

We have

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

\Rightarrow sin^{- 1} \frac{1}{2} + cos^{- 1} x = \frac{π}{2} \Rightarrow \frac{π}{6} + cos^{- 1} x = \frac{π}{2}

∴ cos^{- 1} x = \frac{π}{3} ∴ x = cos \frac{π}{3} = \frac{1}{2}

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Question Text	If $sin (sin^{- 1} \frac{1}{2} + cos^{- 1} x) = 1$ , then find the value of $x$ .
Answer Type	Text solution:1
Upvotes	151