if-A-B-pi-4-so-proof-1-tan-A-1-tan-B-2-

Question Number 21142 by oyshi last updated on 14/Sep/17

i f A + B = \frac{π}{4}

s o p r o o f (1 + \tan A) (1 + \tan B) = 2

Commented by dioph last updated on 14/Sep/17

\tan A + B = 1

\frac{\tan A + \tan B}{1 - \tan A \tan B} = 1

\tan A + \tan B = 1 - \tan A \tan B

\tan A + \tan B + \tan A \tan B + 1 = 2

(1 + \tan A) (1 + \tan B) = 2

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