What is the general solution for csc^2(x)=5csc(x) ?

The general solution for csc^2(x)=5csc(x) is x=0.20135…+2pin,x=pi-0.20135…+2pin

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csc^2(x)=5csc(x)

csc^{2} (x) = 5 csc (x)

x = 0.20135 \dots + 2 πn, x = π - 0.20135 \dots + 2 πn

Solution steps

csc^{2} (x) = 5 csc (x)

Solve by substitution

csc (x) = 5, csc (x) = 0

csc (x) = 5 : x = arccsc (5) + 2 πn, x = π - arccsc (5) + 2 πn

csc (x) = 0 :

No Solution

Combine all the solutions

x = arccsc (5) + 2 πn, x = π - arccsc (5) + 2 πn

Show solutions in decimal form

x = 0.20135 \dots + 2 πn, x = π - 0.20135 \dots + 2 πn

cos (4 θ) = 0

t, L {sin (2 t)} = \frac{2}{s ^{2} + 4}

2 sec^{2} (x) + tan (x) = 5

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

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

What is the general solution for csc^2(x)=5csc(x) ?
The general solution for csc^2(x)=5csc(x) is x=0.20135…+2pin,x=pi-0.20135…+2pin