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# half angles watch

1. It gets worse all the time...

By substituting x = 45º in the formula

tan x = (2tan x/2)/(1-tan^2 x/2)

solve the quadratic in tan 22.5 and hence show that tan 22.5 = sqrt2 -1

----

I don't even know how to start. If I substitute I end up with

tan 25 (1-tan^2 22.5) = 2 tan 22.5

which leads me to believe I've got it all wrong!

help...

jorge
2. (Original post by Jorge)
It gets worse all the time...

By substituting x = 45º in the formula

tan x = (2tan x/2)/(1-tan^2 x/2)

solve the quadratic in tan 22.5 and hence show that tan 22.5 = sqrt2 -1

----

I don't even know how to start. If I substitute I end up with

tan 25 (1-tan^2 22.5) = 2 tan 22.5

which leads me to believe I've got it all wrong!

help...

jorge

You know that tan45 = 1

so the equation becomes:

(2tan(22.5))/(1-tan^2(22.5)) = 1

Now let tan22.5 = X (just for making your algebra look neater)

=> 2X/(1-X^2) = 1
=> 1-X^2 = 2X
=> X^2 + 2X - 1 = 0
=> X = [-2 +/ root(8)]/2
=> tan(22.5) = -1 +/- root(2)

Here we take the positive sign because tan(22.5) > 0

=> tan(22.5) = root(2) - 1

Euclid.
3. Thanks Euclid
4. (Original post by Jorge)
Thanks Euclid
No problem.

Euclid.

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