What is the general solution for 4sin(x/2)-1=1 ?

The general solution for 4sin(x/2)-1=1 is x= pi/3+4pin,x=(5pi)/3+4pin

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4sin(x/2)-1=1

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

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

Solution steps

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

Move

1

to the right side

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

Divide both sides by

4

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

General solutions for

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

\frac{x}{2} = \frac{π}{6} + 2 πn, \frac{x}{2} = \frac{5 π}{6} + 2 πn

Solve

\frac{x}{2} = \frac{π}{6} + 2 πn : x = \frac{π}{3} + 4 πn

Solve

\frac{x}{2} = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{3} + 4 πn

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

- sin (θ) = \frac{1}{2}

3 sec (θ) + 6 = 0

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

8 sin (x) + 6 cos (x) = 8

4 sin (x) + 5 = 0

What is the general solution for 4sin(x/2)-1=1 ?
The general solution for 4sin(x/2)-1=1 is x= pi/3+4pin,x=(5pi)/3+4pin