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

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

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

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

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

Solution steps

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

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

2 cos (θ) + 1 = 0

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

sin (16 5^{\circ})

1 - 2 sin (θ) = cos (2 θ)

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