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Find the value of x which satisfy the equation { sin }^{ -1 }x

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Find the value of x which satisfy the equation $s in^{- 1} x + s in^{- 1} (1 - x) = cos^{- 1} x$

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Find the value of x which satisfy the equation

s in^{- 1} x + s in^{- 1} (1 - x) = cos^{- 1} x

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11 mins ago

Text solutionVerified

From the given equation, we have

sin (s in^{- 1} x + s in^{- 1} (1 - x)) = sin (cos^{- 1} x)

\Rightarrow sin (sin^{- 1} x) cos (sin^{- 1} (1 - x)) + cos (- s i n^{- 1} x) sin (sin^{- 1} (1 - x)) = sin (cos^{- 1} x)

\Rightarrow x 1 - (1 - x)^{2} + (1 - x) 1 - x^{2} = 1 - x^{2}

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

\Rightarrow x (2 x - x^{2} - 1 - x^{2}) = 0

\Rightarrow x = 0

2 x - x^{2} = 1 - x^{2}

\Rightarrow x = 0

x = \frac{1}{2}

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Question Text	Find the value of x which satisfy the equation $s in^{- 1} x + s in^{- 1} (1 - x) = cos^{- 1} x$
Answer Type	Text solution:1
Upvotes	150