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

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

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

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

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

Solution steps

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

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

3 sin (x) + 6 cos (x) = 4

3 tan (2 x + 1) = 2

\frac{1}{( 1 + tan ( a ) )} = cot (a)

tan (2 x) - 2 = 3 tan (x)

sin (x - \frac{π}{6}) = 0

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