Solve $tan^{- 1} x > cot^{- 1} x$ .

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tan^{- 1} x > cot^{- 1} x

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Text solutionVerified

Given,

tan^{- 1} x > cot^{- 1} x \Rightarrow tan (tan^{- 1} x) > tan (cot^{- 1} x)

\Rightarrow tan (tan^{- 1} x) > tan (tan^{- 1} \frac{1}{x})

\Rightarrow x > \frac{1}{x} \Rightarrow x^{2} > 1

(for x>0)

x > \pm 1

\Rightarrow x \in (1, \infty)

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