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

$$ifA+B=\frac{\pi }{4}$$$$soproof(1+\tan A)(1+\tan B)=2$$

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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