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What is tan inverse +cot inverse equal . Plz do tell the solution of proving
tan-1x + cot-1x = π/2, x ∈ R Proof- Let tan-1 x = y⇒ x = tan y⇒ x = Cot (π/2 - y) ['.' tan θ = cot(π/2 - θ)]⇒ cot-1x = cot-1[Cot (π/2 - y)]⇒ cot-1x = π/2 - y⇒ cot-1 x + y = π/2⇒ cot-1 x + tan-1x = π/2
tan-1x + cot-1x = π/2, x ∈ R
Proof-
Let tan-1 x = y
⇒ x = tan y
⇒ x = Cot (π/2 - y) ['.' tan θ = cot(π/2 - θ)]
⇒ cot-1x = cot-1[Cot (π/2 - y)]
⇒ cot-1x = π/2 - y
⇒ cot-1 x + y = π/2
⇒ cot-1 x + tan-1x = π/2
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