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

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

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

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

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

Solution steps

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

Move

2

to the right side

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

Divide both sides by

2

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

General solutions for

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

\frac{1}{2} x = \frac{π}{4} + 2 πn, \frac{1}{2} x = \frac{3 π}{4} + 2 πn

Solve

\frac{1}{2} x = \frac{π}{4} + 2 πn : x = \frac{π}{2} + 4 πn

Solve

\frac{1}{2} x = \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

11 sin (b) - 1 = 3 sin (b) - 1

tan^{2} (x) - 5 tan (x) + 6 = 0

3 tan (\frac{x}{4}) - 3 = 0

sin^{2} (3 x) = 1

2 - - 1 - 6 sin (x) = - 4 sin (x)

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