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

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

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2-2csc^2(x)=-csc^2(x)+csc(x)

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

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

Solution steps

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

Solve by substitution

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

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

csc (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

2 sin (x) + sin (2 x) + cos (x) = - 1

4 cot (x) + 5 = 1

\frac{1}{36} + cos^{2} (θ) = 1

2 sin (x) - (2 + 2) = - 2 csc (x)

5 cos (A) - 10 = 0

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