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What is tan inverse +cot inverse equal . Plz do tell the solution of proving

What is tan inverse +cot inverse equal . Plz do tell the solution of proving

Grade:11

1 Answers

Arun
25763 Points
4 years ago

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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