Tan(phi per 4 - A) per tan(phi per 4 +A) = 1 per 4

[tex] \frac{tan(\frac{\pi}{4})-A}{tan(\frac{\pi}{4})+A} = \frac{1}{4} \\ \frac{tan(45-A)}{tan(45+A)} = \frac{1}{4} \\ 4(tan(45-A)) = tan(45+A) \\ 4(\frac{tan(45)-tan(A)}{1+tan(45)tan(A)} = \frac{tan(45)+tan(A)}{1-tan(45)tan(A)} \\ 4(\frac{1-tan(A)}{1+(1)tan(A)} = \frac{1+tan(A)}{1-(1)tan(A)} \\ \frac{4-4tan(A)}{1+tan(A)} - \frac{1+tan(A)}{1-tan(A)} = 0 \\ \frac{4-4tan^2(A)}{1-tan(A)} = 0 \\ 4-4tan^2(A) = 0 \\ tan^2(A) = 1 \\ tan(A) = +-1 [/tex]

Namun, tan(A) = 1 tidak memungkinkan, karena [tex] \frac{1 + tan(A)}{1 - tan(A)} [/tex] akan menjadi tidak real.

Jadi, penyelesaiannya
tan(A) = -1
tan(A) = tan 135°
A = 135° ± k.180°