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    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
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    (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.
    • Thread Starter
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    Thanks Euclid
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    (Original post by Jorge)
    Thanks Euclid
    No problem.

    Euclid.
 
 
 
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