What is the general solution for 2cos(x/2)-sqrt(2)=0,0<= x<2pi ?

The general solution for 2cos(x/2)-sqrt(2)=0,0<= x<2pi is x= pi/2

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2cos(x/2)-sqrt(2)=0,0<= x<2pi

2 cos (\frac{x}{2}) - 2 = 0, 0 \leq x < 2 π

x = \frac{π}{2}

Solution steps

2 cos (\frac{x}{2}) - 2 = 0, 0 \leq x < 2 π

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{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

Solutions for the range

0 \leq x < 2 π

x = \frac{π}{2}

cos (\frac{x}{4}) = - \frac{2}{2}

tan (θ) = \frac{- 4}{4}

tan (x) = \frac{12}{20}

2 sin (x) + sin (x) = 0

15 cos (x) = 0

What is the general solution for 2cos(x/2)-sqrt(2)=0,0<= x<2pi ?
The general solution for 2cos(x/2)-sqrt(2)=0,0<= x<2pi is x= pi/2