Tan [x-pi/4] = tanx - 1

Solve for x:

-tan (π/4 - x) = tan (x) - 1

Subtract tan (x) - 1 from both sides:

1 - tan (π/4 - x) - tan (x) = 0

Simplify and substitute y = - tan (x).

1 - tan (π/4 - x) - tan (x) = (-tan (x) (1 - tan (x))) / (-tan (x) - 1)

= (y (y + 1)) / (y - 1):

(y (y + 1)) / (y - 1) = 0

Multiply both sides by y - 1:

y (y + 1) = 0

Split into two equations:

y = 0 or y + 1 = 0

Substitute back for y = - tan (x):

-tan (x) = 0 or y + 1 = 0

Multiply both sides by - 1:

tan (x) = 0 or y + 1 = 0

Take the inverse tangent of both sides:

x = π n_1 for n_1 element Z

or y + 1 = 0

Subtract 1 from both sides:

x = π n_1 for n_1 element Z

or y = - 1

Substitute back for y = - tan (x):

x = π n_1 for n_1 element Z

or - tan (x) = - 1

Multiply both sides by - 1:

x = π n_1 for n_1 element Z

or tan (x) = 1

Take the inverse tangent of both sides:

Answer: x = π n_1 for n_1 element Z or x = π n_2 + π/4 for n_2 element Z