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

The general solution for 2cos(2x)=1 is x= pi/6+pin,x=(5pi)/6+pin

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2cos(2x)=1

2 cos (2 x) = 1

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Solution steps

2 cos (2 x) = 1

Divide both sides by

2

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

General solutions for

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

2 x = \frac{π}{3} + 2 πn, 2 x = \frac{5 π}{3} + 2 πn

Solve

2 x = \frac{π}{3} + 2 πn : x = \frac{π}{6} + πn

Solve

2 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{6} + πn

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

2 cos (x) + 1 = 0

cos^{2} (θ) - sin^{2} (θ) = 1 + sin (θ)

cos^{2} (x) + cos (x) = 0

cos (2 x) sin (x) = 0

2 sin (2 x) + 1 = 0

What is the general solution for 2cos(2x)=1 ?
The general solution for 2cos(2x)=1 is x= pi/6+pin,x=(5pi)/6+pin