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The value of x which satisfies { ( ^{ -1 }{ x } ) } = { (

Question

The value of $x$ which satisfies $sin (cot^{- 1} x) = cos (tan^{- 1} (1 + x))$ is ?

- \frac{1}{2}

\frac{1}{2}

- 1

1

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Harper Discussed

The value of

x

which satisfies

sin (cot^{- 1} x) = cos (tan^{- 1} (1 + x))

is ?

11 mins ago

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11 mins ago

Text solutionVerified

co t^{- 1} x = s i n^{- 1} (\frac{1}{x ^{2} + 1})

...[1]

t a n^{- 1} x = co s^{- 1} (\frac{1}{x ^{2} + 1})

⟹ t a n^{- 1} (1 + x) = co s^{- 1} (\frac{1}{( 1 + x ) ^{2} + 1})

...[2]

s in (co t^{- 1} x) = cos (t a n^{- 1} (1 + x)))

⟹ s in (s i n^{- 1} (\frac{1}{x ^{2} + 1})) = cos (co s^{- 1} (\frac{1}{( 1 + x ) ^{2} + 1}))

...(from [1] and[2])

⟹ \frac{1}{x ^{2} + 1} = \frac{1}{( 1 + x ) ^{2} + 1}

⟹ 2 x + 1 = 0

⟹ x = \frac{- 1}{2}

Hence, the answer is option (A).

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Question Text	The value of $x$ which satisfies $sin (cot^{- 1} x) = cos (tan^{- 1} (1 + x))$ is ?
Answer Type	Text solution:1
Upvotes	150