What is the general solution for cot^2(x)-3csc(x)+3=0 ?

The general solution for cot^2(x)-3csc(x)+3=0 is x= pi/6+2pin,x=(5pi)/6+2pin,x= pi/2+2pin

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

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

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 = 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

2 sin^{2} (\frac{θ}{2} - \frac{π}{6}) - 1 = 0

cos^{2} (3 6^{\circ}) - sin^{2} (3 6^{\circ}) = cos (x)

23 cos (x) = - 17 - cos (x)

8 cos^{2} (θ) + 14 cos (θ) - 11 = 8 cos (θ) - 6

tan (x) cos (x) + cos (x) = 0

What is the general solution for cot^2(x)-3csc(x)+3=0 ?
The general solution for cot^2(x)-3csc(x)+3=0 is x= pi/6+2pin,x=(5pi)/6+2pin,x= pi/2+2pin