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

The general solution for 1-cos(x)=2+cos(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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1-cos(x)=2+cos(x)

1 - cos (x) = 2 + cos (x)

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

1 - cos (x) = 2 + cos (x)

Solve by substitution

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

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

(1 + cos (4 x)) sin (4 x) = 2 cos^{2} (2 x)

\frac{5 sin ( x ) + 6}{sin ( x )} = 17

tan^{2} (x) sec (x) - 1 = 0

sin^{2} (x) + cos^{4} (x) = 2

(1 + sin^{2} (x)) = (4 cos (x))^{2}

What is the general solution for 1-cos(x)=2+cos(x) ?
The general solution for 1-cos(x)=2+cos(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin