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

The general solution for csc^2(x)-cot(x)=1 is x= pi/4+pin,x= pi/2+pin

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

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

x = \frac{π}{4} + πn, x = \frac{π}{2} + πn

Solution steps

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

Subtract

1

from both sides

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

Rewrite using trig identities

- cot (x) + cot^{2} (x) = 0

Solve by substitution

cot (x) = 1, cot (x) = 0

cot (x) = 1 : x = \frac{π}{4} + πn

cot (x) = 0 : x = \frac{π}{2} + πn

Combine all the solutions

x = \frac{π}{4} + πn, x = \frac{π}{2} + πn

cos (2 x) - 3 sin (x) = 2

tan (θ) = 9

sin (θ) - 1 = - 1

3 + sin (x) = 3 cos^{2} (x)

cot (θ) = 3

What is the general solution for csc^2(x)-cot(x)=1 ?
The general solution for csc^2(x)-cot(x)=1 is x= pi/4+pin,x= pi/2+pin