What is the general solution for 2cos(x/2)+sqrt(2)=0 ?

The general solution for 2cos(x/2)+sqrt(2)=0 is x=(3pi)/2+4pin,x=(5pi)/2+4pin

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2cos(x/2)+sqrt(2)=0

2 cos (\frac{x}{2}) + 2 = 0

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

Solution steps

2 cos (\frac{x}{2}) + 2 = 0

Move

2

to the right side

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

Divide both sides by

2

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

sin (2 x) + 2 cos (x) = 0, 0 \leq x \leq 2 π

cos (x) = \frac{8.5}{9.9}

cos^{3} (x) = - cos^{2} (x)

3 tan (2 x - π) + 1 = 0

3 sec (2 x) + 2 = 0

What is the general solution for 2cos(x/2)+sqrt(2)=0 ?
The general solution for 2cos(x/2)+sqrt(2)=0 is x=(3pi)/2+4pin,x=(5pi)/2+4pin