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

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

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

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

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

Solution steps

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

Multiply both sides by

sin (x)

1 = 2 sin (x)

Switch sides

2 sin (x) = 1

Divide both sides by

2

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

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

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

General solutions for

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

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

0 = sec (\frac{π x}{4})

3 cos^{2} (x) + 2 cos (x) - 1 = 0

arctan (θ) = - 2

sin (3 x) - sin (x) = sin (3 x - x)

sin (a) = - \frac{3}{2}

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