What is the general solution for 6cos(2x)=3sqrt(2) ?

The general solution for 6cos(2x)=3sqrt(2) is x= pi/8+pin,x=(7pi)/8+pin

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6cos(2x)=3sqrt(2)

6 cos (2 x) = 32

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

Solution steps

6 cos (2 x) = 32

Divide both sides by

6

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} (x) - sin^{2} (x) = 0

10 cos (x) + 4 = 10

x, arctan (x) = \frac{π}{4}

cos (2 θ) + 3 cos (θ) = 1

coth (x) = 1

What is the general solution for 6cos(2x)=3sqrt(2) ?
The general solution for 6cos(2x)=3sqrt(2) is x= pi/8+pin,x=(7pi)/8+pin