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

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

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csc^2(x)+csc(x)-1=1

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

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

Solution steps

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

Solve by substitution

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

csc (x) = 1 : x = \frac{π}{2} + 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}{2} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

\frac{a}{sin ( a )} = \frac{a}{sin ( B )}

cos (θ) = 1, 0^{\circ} \leq θ \leq 18 0^{\circ}

x, z = cos (2 x + y)

16 tan^{2} (x) - 1 = 0

sin^{2} (x) - sin (x) = 0, 0 \leq x \leq 2 π

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