What is the general solution for 8cos(2x)=4sqrt(3) ?

The general solution for 8cos(2x)=4sqrt(3) is x= pi/(12)+pin,x=(11pi)/(12)+pin

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8cos(2x)=4sqrt(3)

8 cos (2 x) = 43

x = \frac{π}{12} + πn, x = \frac{11 π}{12} + πn

Solution steps

8 cos (2 x) = 43

Divide both sides by

8

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

General solutions for

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

2 x = \frac{π}{6} + 2 πn, 2 x = \frac{11 π}{6} + 2 πn

Solve

2 x = \frac{π}{6} + 2 πn : x = \frac{π}{12} + πn

Solve

2 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{12} + πn

x = \frac{π}{12} + πn, x = \frac{11 π}{12} + πn

cos^{2} (θ) - sin^{2} (θ) = 1

2 cos^{2} (x) = 1 - cos (x)

cos^{3} (x) = cos^{3} (x) csc (x)

- \frac{1}{2} = sin (θ)

2 sin (2 x) + 3 = 2

What is the general solution for 8cos(2x)=4sqrt(3) ?
The general solution for 8cos(2x)=4sqrt(3) is x= pi/(12)+pin,x=(11pi)/(12)+pin