What is the general solution for cot^2(x)-3csc(x)=-3 ?

The general solution for cot^2(x)-3csc(x)=-3 is x= pi/6+2pin,x=(5pi)/6+2pin,x= pi/2+2pin

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cot^2(x)-3csc(x)=-3

cot^{2} (x) - 3 csc (x) = - 3

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

Solution steps

cot^{2} (x) - 3 csc (x) = - 3

Subtract

- 3

from both sides

cot^{2} (x) - 3 csc (x) + 3 = 0

Rewrite using trig identities

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

Solve by substitution

csc (x) = 2, csc (x) = 1

csc (x) = 2 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

csc (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

tan (4 x) = 0

2 cot (x) = csc (x)

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

5 tan^{2} (θ) - tan (θ) + 12 = 8 tan (θ) + 8

16 sin^{2} (θ) - 4 = 0

What is the general solution for cot^2(x)-3csc(x)=-3 ?
The general solution for cot^2(x)-3csc(x)=-3 is x= pi/6+2pin,x=(5pi)/6+2pin,x= pi/2+2pin