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

The general solution for cos(x/2)=-(sqrt(2))/2 is x=(3pi)/2+4pin,x=(5pi)/2+4pin

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

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

x = \frac{3 π}{2} + 4 πn, x = \frac{5 π}{2} + 4 πn

Solution steps

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

General solutions for

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

\frac{x}{2} = \frac{3 π}{4} + 2 πn, \frac{x}{2} = \frac{5 π}{4} + 2 πn

Solve

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

Solve

\frac{x}{2} = \frac{5 π}{4} + 2 πn : x = \frac{5 π}{2} + 4 πn

x = \frac{3 π}{2} + 4 πn, x = \frac{5 π}{2} + 4 πn

0 = 1 - cos (2 x)

sec^{2} (x) + 2 = 3 sec (x)

cos (x) - 1 = - cos (x)

2 cos^{2} (x) = 3

9 tan (2 x) - 9 cot (x) = 0

What is the general solution for cos(x/2)=-(sqrt(2))/2 ?
The general solution for cos(x/2)=-(sqrt(2))/2 is x=(3pi)/2+4pin,x=(5pi)/2+4pin