8 arctan[sqrt(2) - 1] =why do you get the answer that you get? Don't undertand. Thanks.
+9665 Let a = arctan(\(\sqrt2 - 1\))
Double angle formulae:
\(\tan(2a)\\=\dfrac{2\tan a}{1-\tan ^2 a}\\=\dfrac{2(\sqrt2 - 1)}{1-(\sqrt2 - 1)^2}\\ = \dfrac{2\sqrt2 - 2}{1-(2+1-2\sqrt2)}\\ =\dfrac{2\sqrt2 - 2}{1-2-1+2\sqrt2}\\ =\dfrac{2\sqrt2 - 2}{2\sqrt2 - 2}\\ =1\)
When tan(2a) = 1, 2a = 45 degrees. Therefore a = 22.5 degrees or pi/8 radians.
8(arctan(sqrt(2)-1)) = 8(pi/8) = pi.
