Prove-the-identity-tan-1-x-cot-1-x-pi-2-

Question Number 130589 by bramlexs22 last updated on 27/Jan/21

Prove the identity \tan^{- 1} (x) + \cot^{- 1} (x) = π / 2

Answered by EDWIN88 last updated on 27/Jan/21

I f f (x) = \tan^{- 1} (x) + \cot^{- 1} (x)

t h e n f^{'} (x) = \frac{1}{1 + x^{2}} - \frac{1}{1 + x^{2}} = 0

f o r \forall v a l u e s o f x . T h e r e f o r e

f (x) = C, a c o n s t a n t .

T o d e t e r m i n e t h e v a l u e o f C

w e p u t x = 1 s i n c e w e c a n e v a l u a t e

f (1) e x a c t l y . T h e n C = f (1) =

\tan^{- 1} (1) + \cot^{- 1} (1) = \frac{π}{4} + \frac{π}{4} = \frac{π}{2}

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