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

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

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sin(1/2 x)+1=0

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

x = 3 π + 4 πn

Solution steps

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

Move

1

to the right side

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

General solutions for

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

\frac{1}{2} x = \frac{3 π}{2} + 2 πn

Solve

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

x = 3 π + 4 πn

4 cos^{2} (x) + 8 cos (x) + 4 = 0

4 sin (x) cos (x) = 22 cos (x)

t, x = cos^{2} (t)

sin (x) = \frac{24}{27}

cot^{2} (x) = 0

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