What is the general solution for cos(2x)+cos(2x)+1=0 ?

The general solution for cos(2x)+cos(2x)+1=0 is x= pi/3+pin,x=(2pi)/3+pin

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cos(2x)+cos(2x)+1=0

cos (2 x) + cos (2 x) + 1 = 0

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

Solution steps

cos (2 x) + cos (2 x) + 1 = 0

Simplify

cos (2 x) + cos (2 x) + 1 : 2 cos (2 x) + 1

2 cos (2 x) + 1 = 0

Move

1

to the right side

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

Solve

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

Solve

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

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

(cos^{2} (x) + cos (x)) \cdot (sin (x) + sin^{3} (x)) = 0

arccos (x) - arcsin (x) = arcsin (1 - x)

sin^{2} (x) = ∣ sin (x) ∣

1 - cos^{2} (x) - sin^{22} (x) = 0

cos (\frac{x}{4}) sin (\frac{x}{4}) = 3 sin (\frac{x}{4}) cos (\frac{x}{4})

What is the general solution for cos(2x)+cos(2x)+1=0 ?
The general solution for cos(2x)+cos(2x)+1=0 is x= pi/3+pin,x=(2pi)/3+pin