tan−1x+cot−1x=2π ,x∈R∙

Given tan−1+cot−1x Let tan−1x=A ⟹tanA=x⟹cot(2π−A)=x⟹cot−1 x=2π−A ⟹tan−1x+cot−1x ⟹A+2π−A⟹2π

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{ ^{ - 1}}x + { ^{ - 1}}x = { 2},x R^

Question

$tan^{- 1} x + cot^{- 1} x = \frac{π}{2}, x \in R ∙$

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Henry Discussed

tan^{- 1} x + cot^{- 1} x = \frac{π}{2}, x \in R ∙

12 mins ago

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12 mins ago

Given

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

Let

tan^{- 1} x = A

⟹ tan A = x

⟹ cot (\frac{π}{2} - A) = x

⟹ cot^{- 1} x = \frac{π}{2} - A

⟹ tan^{- 1} x + cot^{- 1} x

⟹ A + \frac{π}{2} - A

⟹ \frac{π}{2}

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