What is the general solution for csc(x)=6 ?

The general solution for csc(x)=6 is x=0.16744…+2pin,x=pi-0.16744…+2pin

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csc(x)=6

csc (x) = 6

x = 0.16744 \dots + 2 πn, x = π - 0.16744 \dots + 2 πn

Solution steps

csc (x) = 6

Apply trig inverse properties

x = arccsc (6) + 2 πn, x = π - arccsc (6) + 2 πn

Show solutions in decimal form

x = 0.16744 \dots + 2 πn, x = π - 0.16744 \dots + 2 πn

(sin (x))^{s i n (x)} = 2

cos^{2} (x) + \frac{1}{2} + sin^{2} (x) + \frac{1}{2} = 2

sin^{2} (x) - 2 cos (x) - 2 = 0

\frac{1}{2} tan^{2} (x) = 1 - sec (x)

sin (2 x) = sin^{2} (x)

What is the general solution for csc(x)=6 ?
The general solution for csc(x)=6 is x=0.16744…+2pin,x=pi-0.16744…+2pin