What is the general solution for sqrt(2)sin(x/2)-1=0 ?

The general solution for sqrt(2)sin(x/2)-1=0 is x= pi/2+4pin,x=(3pi)/2+4pin

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sqrt(2)sin(x/2)-1=0

2 sin (\frac{x}{2}) - 1 = 0

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

Solution steps

2 sin (\frac{x}{2}) - 1 = 0

Move

1

to the right side

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

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

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

2 tan^{2} (t) = - 3 sec (t)

tan^{2} (x) + 3 = 0

4 cos (θ) + 1 = 0

cos (a) = \frac{3}{- 6}

What is the general solution for sqrt(2)sin(x/2)-1=0 ?
The general solution for sqrt(2)sin(x/2)-1=0 is x= pi/2+4pin,x=(3pi)/2+4pin