What is the general solution for 1=1-2arctan((1-2-C)/(1-C)) ?

The general solution for 1=1-2arctan((1-2-C)/(1-C)) is C=-1

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1=1-2arctan((1-2-C)/(1-C))

1 = 1 - 2 arctan (\frac{1 - 2 - C}{1 - C})

C = - 1

Solution steps

1 = 1 - 2 arctan (\frac{1 - 2 - C}{1 - C})

Switch sides

1 - 2 arctan (\frac{1 - 2 - C}{1 - C}) = 1

Subtract

1

from both sides

1 - 2 arctan (\frac{1 - 2 - C}{1 - C}) - 1 = 1 - 1

Simplify

- 2 arctan (\frac{1 - 2 - C}{1 - C}) = 0

Divide both sides by

- 2

arctan (\frac{1 - 2 - C}{1 - C}) = 0

Apply trig inverse properties

\frac{1 - 2 - C}{1 - C} = 0

Solve

\frac{1 - 2 - C}{1 - C} = 0 : C = - 1

C = - 1

x, 1 + 2 sin (x) = 0

sin (x) = \frac{- 5}{13}

sin^{2} (θ) - cos^{2} (θ) + cos (θ) = 0

3 sin^{2} (x) = 9 cos^{2} (x)

sin (\frac{1}{2 x}) = - 1

What is the general solution for 1=1-2arctan((1-2-C)/(1-C)) ?
The general solution for 1=1-2arctan((1-2-C)/(1-C)) is C=-1