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

The general solution for 2cos(3x)=-sqrt(2) is x= pi/4+(2pin)/3 ,x=(5pi}{12}+\frac{2pin)/3

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

2 cos (3 x) = - 2

x = \frac{π}{4} + \frac{2 πn}{3}, x = \frac{5 π}{12} + \frac{2 πn}{3}

Solution steps

2 cos (3 x) = - 2

Divide both sides by

2

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

General solutions for

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

3 x = \frac{3 π}{4} + 2 πn, 3 x = \frac{5 π}{4} + 2 πn

Solve

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

Solve

3 x = \frac{5 π}{4} + 2 πn : x = \frac{5 π}{12} + \frac{2 πn}{3}

x = \frac{π}{4} + \frac{2 πn}{3}, x = \frac{5 π}{12} + \frac{2 πn}{3}

2 - 2 cos (x) = 0

cos (x) = 2 - cos (x)

cos^{2} (x) - \frac{7}{2} cos (x) - 2 = 0

tan (x) sin^{2} (x) - 3 tan (x) = 0

sec^{2} (θ) - 6 = - 4

What is the general solution for 2cos(3x)=-sqrt(2) ?
The general solution for 2cos(3x)=-sqrt(2) is x= pi/4+(2pin)/3 ,x=(5pi}{12}+\frac{2pin)/3