Jika (1+tan α ) (1+tan β )=2, maka nilai tan (α+β) =

[tex]\displaystyle (1+\tan a)(1+\tan b)=2\\1+\tan a+\tan b+\tan a\tan b=2\\\tan a+\tan b+\tan a\tan b=1\\\tan a+\tan b=1-\tan a\tan b\\\frac{\tan a+\tan b}{1-\tan a\tan b}=1\\\boxed{\boxed{\tan(a+b)=1}}[/tex]