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Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

Number of sol...

Question

Number of solutions of the equation $2 e^{| x |} {tan}^{- 1} | x | = 1$ is

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Solution

$2 {tan}^{- 1} (| x |) = e^{- | x |}$

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2 e^{| x |} {tan}^{- 1} (| x |) = 1

t a n^{- 1} (x - 1) + t a n^{- 1} (x) + t a n^{- 1} (x + 1) = t a n^{- 1} (3 x)

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t a n^{- 1} (x + 1) + t a n^{- 1} x + t a n^{- 1} (x - 1) = π - t a n^{- 1} 3

t a n^{- 1} (x + 1) + t a n^{- 1} x + t a n^{- 1} (x - 1) = π - t a n^{- 1} 3

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