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

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

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cos(2x)= 1/(sqrt(2))

cos (2 x) = \frac{1}{2}

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

Solution steps

cos (2 x) = \frac{1}{2}

Simplify

\frac{1}{2} : \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

cos^{2} (x) = 2 + 2 sin (x)

arccsc (\frac{2 3}{3})

csc (θ) + 2 = 0

csc (x) = 2

cos (\frac{5 π}{6})

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