Find the value of x if,sin{sin−151+cos−1x}=1

sin{sin−151+cos−1x}=1⇒sin−151+cos−1x=sin−11⇒sin−151+cos−1x=2π⇒sin−151=2π−cos−1xWe know that sin−1x+cos−1x=2π⇒sin−151=sin−1x∴x=51

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Find the value of x if, sin{ { sin }^{ -1 } { 1 }{ 5 } +{ co

Question

Find the value of x if,

$s in {s in^{- 1} \frac{1}{5} + cos^{- 1} x} = 1$

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Evelyn Discussed

Find the value of x if,

s in {s in^{- 1} \frac{1}{5} + cos^{- 1} x} = 1

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12 mins ago

sin {sin^{- 1} \frac{1}{5} + cos^{- 1} x} = 1

\Rightarrow sin^{- 1} \frac{1}{5} + cos^{- 1} x = sin^{- 1} 1

\Rightarrow sin^{- 1} \frac{1}{5} + cos^{- 1} x = \frac{π}{2}

\Rightarrow sin^{- 1} \frac{1}{5} = \frac{π}{2} - cos^{- 1} x

We know that

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

\Rightarrow sin^{- 1} \frac{1}{5} = sin^{- 1} x

∴ x = \frac{1}{5}

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Question Text	Find the value of x if, $s in {s in^{- 1} \frac{1}{5} + cos^{- 1} x} = 1$
Answer Type	Text solution:1
Upvotes	150