Trigonometria

Se a (alfa) + b (beta) = pi/4, então
(1+tga)(1+tgb) é igual a:

Gabarito: 2

Pfv expliquem a resolução

Olá laudi08! 

[latex]\\\alpha=\frac{\pi}{4}-\beta\\\\ \rightarrow\tan\alpha = \tan\left (\frac{\pi}{4}-\beta \right )=\frac{\tan\frac{\pi}{4}-\tan\beta}{1+\tan\frac{\pi}{4}\tan\beta} =\frac{1-\tan\beta}{1+\tan\beta}\\\\ \rightarrow 1+\tan\alpha = 1 +\frac{1-\tan\beta}{1+\tan\beta} = \frac{2}{1+\tan\beta}\\\\ \rightarrow\boxed{\left ( 1+\tan\alpha \right ).\left ( 1+\tan\beta\right )=2}[/latex]