What is the general solution for 2sin(x/2)-sqrt(2)=0 ?

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

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2sin(x/2)-sqrt(2)=0

2 sin (\frac{x}{2}) - 2 = 0

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

Solution steps

2 sin (\frac{x}{2}) - 2 = 0

Move

2

to the right side

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

Divide both sides by

2

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

General solutions for

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

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

Solve

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

Solve

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

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

- 3 sin (3 θ) = 0

cos (2 x) = - 3 cos (x) - 2

12 sin^{2} (t) + cos (t) - 1 = 5

sin (x) = \frac{5}{12}

arctan (x) = 2

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