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

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

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

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

x = \frac{3 π}{2} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Subtract

cot^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

csc (x) = - 1, csc (x) = 0

csc (x) = - 1 : x = \frac{3 π}{2} + 2 πn

csc (x) = 0 :

No Solution

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

tan (a) = \frac{141}{101}

sin (x) = - cos^{2} (x)

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

2 csc (θ) = 4 cos (θ)

\frac{6}{5} arccos (\frac{y}{6}) = π

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