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

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

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sqrt(2)cos(2x)=1

2 cos (2 x) = 1

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

Solution steps

2 cos (2 x) = 1

Divide both sides by

2

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 csc^{2} (x) = 1 + cos (x)

6 arccos (5 x) = 5 π

sin (x) + sin (x) cot (x) = 0

arctan (θ) = 1

cos (2 θ) = - \frac{1}{2}, 0 \leq θ \leq 2 π

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