What is the general solution for csc(2x)=sqrt(2) ?

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

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csc(2x)=sqrt(2)

csc (2 x) = 2

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

Solution steps

csc (2 x) = 2

General solutions for

csc (2 x) = 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

sin (4 x) cos (x) - sin (x) cos (4 x) = \frac{3}{2}

7 sin (θ) + 1 = 5 sin (θ)

- 5 cos^{2} (θ) - 4 cos (θ) + 4 = 0

cos (x) = 0.159

sin (2 x) = 1 - cos (2 x)

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