In a right triangle abc, right angled at b, the ratio of ab to ac is 1: root 2.find the value of 2tana/1-tan square a

Since we know that ratio of AB : AC is 1 : √2, then we can more or less use those values for the sides, check the picture below.

so we're really looking for tan(2A).  Let's bear in mind that tan²(θ) is just another way to write [ tan(θ) ]².