What is the general solution for cos(x)=(sqrt(1-cos(x)))/2 ?

The general solution for cos(x)=(sqrt(1-cos(x)))/2 is x=1.16974…+2pin,x=2pi-1.16974…+2pin

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cos(x)=(sqrt(1-cos(x)))/2

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

x = 1.16974 \dots + 2 πn, x = 2 π - 1.16974 \dots + 2 πn

Solution steps

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

Solve by substitution

cos (x) = \frac{- 1 + 17}{8}

cos (x) = \frac{- 1 + 17}{8} : x = arccos (\frac{- 1 + 17}{8}) + 2 πn, x = 2 π - arccos (\frac{- 1 + 17}{8}) + 2 πn

Combine all the solutions

x = arccos (\frac{- 1 + 17}{8}) + 2 πn, x = 2 π - arccos (\frac{- 1 + 17}{8}) + 2 πn

Show solutions in decimal form

x = 1.16974 \dots + 2 πn, x = 2 π - 1.16974 \dots + 2 πn

csc (x) = \frac{7}{4}

2 - 4 cos (A) = 0

6 cos (6 x) = 3

x, sin (x) cos (y) = 0

3 cos (x) - 2 sin (x) = 1

What is the general solution for cos(x)=(sqrt(1-cos(x)))/2 ?
The general solution for cos(x)=(sqrt(1-cos(x)))/2 is x=1.16974…+2pin,x=2pi-1.16974…+2pin