tan 45 = 1, show that tan 22.5 = (sqrt. 2) - 1

[Monkeyseat]

Hi,

Question:



Working:

I have done part (a) no problem, it's part (b) that I'm stuck on. I don't really have any working that I can show. I thought maybe do 1 = (2tanx)/(1 - tan[sup:20ezu2fu]2[/sup:20ezu2fu]x), but I don't know how to solve that.

Any help would be greatly appreciated.

Thanks.

 

[Deleted member 4993]

Working: I have done part (a) no problem, it's part (b) that I'm stuck on. I don't really have any working that I can show. I thought maybe do

1 = (2tanx)/(),

1 - tan[sup:1b2or67t]2[/sup:1b2or67t]x = 2 tan(x)

tan[sup:1b2or67t]2[/sup:1b2or67t]x + 2 tan(x) - 1 = 0

The above is a quadratic equation in 'tan(x)' - solve it by your favorite method.

but I don't know how to solve that.

Are you saying that you dont how to solve for 'x', if you are given

x[sup:1b2or67t]2[/sup:1b2or67t] + 2x - 1 = 0.

 

[Monkeyseat]

Thanks for the help. I've managed to complete the question now.