What is the general solution for csc(x)=7 ?

The general solution for csc(x)=7 is x=0.14334…+2pin,x=pi-0.14334…+2pin

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csc(x)=7

csc (x) = 7

x = 0.14334 \dots + 2 πn, x = π - 0.14334 \dots + 2 πn

Solution steps

csc (x) = 7

Apply trig inverse properties

x = arccsc (7) + 2 πn, x = π - arccsc (7) + 2 πn

Show solutions in decimal form

x = 0.14334 \dots + 2 πn, x = π - 0.14334 \dots + 2 πn

2 cos (θ) sin (θ) + cos (θ) - 2 sin (θ) = 1

sin (2 θ) - cos (θ) - 2 sin (θ) + 1 = 0

2 cos (x) + 1 = 0 - 2, π \leq x \leq 2 π

cos^{3} (x) = - cos (x)

csc (2 x) = 2 sin (2 x), 0 \leq x \leq 2 π

What is the general solution for csc(x)=7 ?
The general solution for csc(x)=7 is x=0.14334…+2pin,x=pi-0.14334…+2pin