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

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

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2cos(2x)+1=0

2 cos (2 x) + 1 = 0

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

Solution steps

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

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

sec (\frac{π}{3})

arctan (1)

tan (\frac{3 π}{2})

cos (- \frac{7 π}{4})

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