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

The general solution for sqrt(2)cos(2x)-1=0 is x= pi/8+pin,x=(7pi)/8+pin

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sqrt(2)cos(2x)-1=0

2 cos (2 x) - 1 = 0

x = \frac{π}{8} + πn, x = \frac{7 π}{8} + 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{2}{2}

General solutions for

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

2 x = \frac{π}{4} + 2 πn, 2 x = \frac{7 π}{4} + 2 πn

Solve

2 x = \frac{π}{4} + 2 πn : x = \frac{π}{8} + πn

Solve

2 x = \frac{7 π}{4} + 2 πn : x = \frac{7 π}{8} + πn

x = \frac{π}{8} + πn, x = \frac{7 π}{8} + πn

2 cos^{2} (t) - cos (t) - 3 = 0

2 cos (4 θ + 20) = 0.8

2 - 2 cos^{2} (\frac{x}{2}) = sin^{2} (x)

sin (θ) = \frac{2}{2}, 0 \leq θ \leq 2 π

x, cos (x) = \frac{2}{3}

What is the general solution for sqrt(2)cos(2x)-1=0 ?
The general solution for sqrt(2)cos(2x)-1=0 is x= pi/8+pin,x=(7pi)/8+pin