What is the general solution for -csc^2(x)=-4/3 ?

The general solution for -csc^2(x)=-4/3 is x= pi/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=(5pi)/3+2pin

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-csc^2(x)=-4/3

- csc^{2} (x) = - \frac{4}{3}

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

- csc^{2} (x) = - \frac{4}{3}

Solve by substitution

csc (x) = \frac{2 3}{3}, csc (x) = - \frac{2 3}{3}

csc (x) = \frac{2 3}{3} : x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

csc (x) = - \frac{2 3}{3} : x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

2 sec (x) + 4 = 0

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

sin (\frac{1}{3} x + \frac{3 π}{2}) = 0

2 cos (x) = 3 sin (x)

4 sin^{2} (θ) - 8 cos (θ) + 1 = 0

What is the general solution for -csc^2(x)=-4/3 ?
The general solution for -csc^2(x)=-4/3 is x= pi/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=(5pi)/3+2pin