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

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

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csc(x)=5

csc (x) = 5

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

Solution steps

csc (x) = 5

Apply trig inverse properties

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

sec^{2} (x) + tan^{2} (x) - 1 = 0

tan^{2} (x) - 3 tan (x) = 0, 0 \leq x < 2 π

tan (θ) = 10

8 sin (θ) - 5 = 3 sin (θ)

2 cos (4 x) + 3 = 0

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