What is the general solution for tan(pi/4+x)=(1-tan(x))/(1+tan(x)) ?

The general solution for tan(pi/4+x)=(1-tan(x))/(1+tan(x)) is x=2pin,x=pi+2pin

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tan(pi/4+x)=(1-tan(x))/(1+tan(x))

tan (\frac{π}{4} + x) = \frac{1 - tan ( x )}{1 + tan ( x )}

x = 2 πn, x = π + 2 πn

Solution steps

tan (\frac{π}{4} + x) = \frac{1 - tan ( x )}{1 + tan ( x )}

Rewrite using trig identities

\frac{cos ( x ) + sin ( x )}{cos ( x ) - sin ( x )} = \frac{1 - tan ( x )}{1 + tan ( x )}

Subtract

\frac{1 - tan ( x )}{1 + tan ( x )}

from both sides

\frac{2 tan ( x ) cos ( x ) + 2 sin ( x )}{( tan ( x ) + 1 ) ( cos ( x ) - sin ( x ) )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

2 tan (x) cos (x) + 2 sin (x) = 0

Rewrite using trig identities

4 sin (x) = 0

Divide both sides by

4

sin (x) = 0

General solutions for

sin (x) = 0

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 2 πn, x = π + 2 πn

cos (x) = \frac{45}{52}

x, cos (2 x) = \frac{m - 1}{m + 1}

6 tan^{2} (x) + 8 = 10

2 sin (x - \frac{π}{4}) + 2 cos (x) = 1

sin^{2} (θ) = 2 cos (θ) + 1

What is the general solution for tan(pi/4+x)=(1-tan(x))/(1+tan(x)) ?
The general solution for tan(pi/4+x)=(1-tan(x))/(1+tan(x)) is x=2pin,x=pi+2pin