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

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

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

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

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

Solution steps

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

Solve by substitution

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

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

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

cos (2 x) = - 1, 0 \leq x \leq 2 π

arccot (x) + arctan (3) = \frac{π}{2}

tan (x) = \frac{9}{7}

5 sin (4 x) = - 10 sin (2 x)

cot^{4} (x) = cot^{4} (x) sin (x)

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