What is the general solution for csc^2(x)+4csc(x)-5=0 ?

The general solution for csc^2(x)+4csc(x)-5=0 is x= pi/2+2pin,x=-0.20135…+2pin,x=pi+0.20135…+2pin

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csc^2(x)+4csc(x)-5=0

csc^{2} (x) + 4 csc (x) - 5 = 0

x = \frac{π}{2} + 2 πn, x = - 0.20135 \dots + 2 πn, x = π + 0.20135 \dots + 2 πn

Solution steps

csc^{2} (x) + 4 csc (x) - 5 = 0

Solve by substitution

csc (x) = 1, csc (x) = - 5

csc (x) = 1 : x = \frac{π}{2} + 2 πn

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

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = arccsc (- 5) + 2 πn, x = π + arccsc (5) + 2 πn

Show solutions in decimal form

x = \frac{π}{2} + 2 πn, x = - 0.20135 \dots + 2 πn, x = π + 0.20135 \dots + 2 πn

90 + 45 cos (\frac{t ^{2}}{18}) - 100 = 0

3 tan^{3} (x) + 3 tan^{2} (x) - tan (x) - 1 = 0

8 sin (x) = 4 cos^{2} (x) - 7

cos (x) - 1 = 0, 0 \leq x \leq 2 π

sin (x) = \frac{4.8}{5.5}

What is the general solution for csc^2(x)+4csc(x)-5=0 ?
The general solution for csc^2(x)+4csc(x)-5=0 is x= pi/2+2pin,x=-0.20135…+2pin,x=pi+0.20135…+2pin