What is the general solution for cot^2(x)-csc(x)-1=0 ?

The general solution for cot^2(x)-csc(x)-1=0 is x= pi/6+2pin,x=(5pi)/6+2pin,x=(3pi)/2+2pin

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

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

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 = 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

16 sin^{4} (θ) - 16 sin^{2} (θ) + 3 = 0

7 sin (\frac{θ}{2}) = - 7 cos (\frac{θ}{2})

p, e^{x} - sin (p \frac{x}{3}) = 0

2 cos (x) + cos (2 x) \cdot 2 = 0

3 sin^{2} (t) - 7 sin (t) - 6 = 0

What is the general solution for cot^2(x)-csc(x)-1=0 ?
The general solution for cot^2(x)-csc(x)-1=0 is x= pi/6+2pin,x=(5pi)/6+2pin,x=(3pi)/2+2pin