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

The general solution for 2cos(3x)=sqrt(2) is x= pi/(12)+(2pin)/3 ,x=(7pi}{12}+\frac{2pin)/3

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2cos(3x)=sqrt(2)

2 cos (3 x) = 2

x = \frac{π}{12} + \frac{2 πn}{3}, x = \frac{7 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{π}{4} + 2 πn, 3 x = \frac{7 π}{4} + 2 πn

Solve

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

Solve

3 x = \frac{7 π}{4} + 2 πn : x = \frac{7 π}{12} + \frac{2 πn}{3}

x = \frac{π}{12} + \frac{2 πn}{3}, x = \frac{7 π}{12} + \frac{2 πn}{3}

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

tan (x) = \frac{- 3}{4}

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

3 cos (θ) = sin (θ)

csc (θ) = \frac{4}{3}

What is the general solution for 2cos(3x)=sqrt(2) ?
The general solution for 2cos(3x)=sqrt(2) is x= pi/(12)+(2pin)/3 ,x=(7pi}{12}+\frac{2pin)/3