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

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

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

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

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

Subtract

1

from both sides

cot^{2} (x) - csc (x) - 1 = 0

Rewrite using trig identities

- 2 - csc (x) + csc^{2} (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{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

x, u = arctan (\frac{x}{y})

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sin^{22} (x) sin^{3} (x) + 6 = 18

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