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Question Number 148289 by saly last updated on 26/Jul/21

Commented by saly last updated on 26/Jul/21

$$heplme$$

Answered by mr W last updated on 26/Jul/21

$$\gamma =\frac{\pi }{2}-(\alpha +\beta )$$$$\tan \gamma =\frac{1}{\tan (\alpha +\beta )}$$$$\tan \alpha \tan \beta +\tan \beta \tan \gamma +\tan \alpha \tan \gamma$$$$=\tan \alpha \tan \beta +\frac{\tan \alpha +\tan \beta }{\tan (\alpha +\beta )}$$$$=\tan \alpha \tan \beta +\frac{\tan \alpha +\tan \beta }{\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }}$$$$=\tan \alpha \tan \beta +1-\tan \alpha \tan \beta$$$$=1$$

Commented by puissant last updated on 26/Jul/21

$$goodsirnice..$$

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