What is the general solution for csc^4(2x)-4=0 ?

The general solution for csc^4(2x)-4=0 is x= pi/8+pin,x=(3pi)/8+pin,x=(5pi)/8+pin,x=(7pi)/8+pin

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csc^4(2x)-4=0

csc^{4} (2 x) - 4 = 0

x = \frac{π}{8} + πn, x = \frac{3 π}{8} + πn, x = \frac{5 π}{8} + πn, x = \frac{7 π}{8} + πn

Solution steps

csc^{4} (2 x) - 4 = 0

Solve by substitution

csc (2 x) = 2, csc (2 x) = - 2, csc (2 x) = 2 i, csc (2 x) = - 2 i

csc (2 x) = 2 : x = \frac{π}{8} + πn, x = \frac{3 π}{8} + πn

csc (2 x) = - 2 : x = \frac{5 π}{8} + πn, x = \frac{7 π}{8} + πn

csc (2 x) = 2 i :

No Solution

csc (2 x) = - 2 i :

No Solution

Combine all the solutions

x = \frac{π}{8} + πn, x = \frac{3 π}{8} + πn, x = \frac{5 π}{8} + πn, x = \frac{7 π}{8} + πn

sin (θ) = \frac{4}{13}

sin (3 x) = - \frac{1}{2}, 0 \leq x \leq 2 π

4 cos (x) - 3 sec (x) = 0

sin (θ) = \frac{11}{61}

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

What is the general solution for csc^4(2x)-4=0 ?
The general solution for csc^4(2x)-4=0 is x= pi/8+pin,x=(3pi)/8+pin,x=(5pi)/8+pin,x=(7pi)/8+pin