What is the general solution for 1-csc^2(x)=-3 ?

The general solution for 1-csc^2(x)=-3 is x= pi/6+2pin,x=(5pi)/6+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

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1-csc^2(x)=-3

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

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

Solve by substitution

csc (x) = 2, csc (x) = - 2

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

csc (x) = - 2 : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

tan^{5} (x) = tan (x)

cos^{2} (x) - 3 cos (x) = - 2

2 cot (x) + 3 = 1

3 tan (θ) - 23 = 3

1 - 2 sin^{2} (x) = sin (x)

What is the general solution for 1-csc^2(x)=-3 ?
The general solution for 1-csc^2(x)=-3 is x= pi/6+2pin,x=(5pi)/6+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin