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

The general solution for cos(x/2)= 1/(sqrt(2)) is x= pi/2+4pin,x=(7pi)/2+4pin

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

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

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

Solution steps

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

Simplify

\frac{1}{2} : \frac{2}{2}

General solutions for

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

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

Solve

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

Solve

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

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

2 \cdot cos (2 x) + 1 = 0

sin (2 x) - cos^{2} (x) = 0

2 sin (\frac{π x}{2}) + 1 = 0

sin (x) = 0.819

tan (x) = 1.1

What is the general solution for cos(x/2)= 1/(sqrt(2)) ?
The general solution for cos(x/2)= 1/(sqrt(2)) is x= pi/2+4pin,x=(7pi)/2+4pin