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

The general solution for sin(2x)= 1/(sqrt(2)) is x= pi/8+pin,x=(3pi)/8+pin

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

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

x = \frac{π}{8} + πn, x = \frac{3 π}{8} + πn

Solution steps

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

Simplify

\frac{1}{2} : \frac{2}{2}

General solutions for

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

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

Solve

2 x = \frac{π}{4} + 2 πn : x = \frac{π}{8} + πn

Solve

2 x = \frac{3 π}{4} + 2 πn : x = \frac{3 π}{8} + πn

x = \frac{π}{8} + πn, x = \frac{3 π}{8} + πn

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

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

2 csc^{2} (x) - 3 csc (x) - 2 = 0

csc (x) = \frac{2}{3}

8 - 7 cos (x) = 6 sin^{2} (x)

What is the general solution for sin(2x)= 1/(sqrt(2)) ?
The general solution for sin(2x)= 1/(sqrt(2)) is x= pi/8+pin,x=(3pi)/8+pin