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

cot (x) + 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

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

21 csc^{2} (2 x) - 5 = 23

4 sin^{2} (\frac{x}{3}) = 1

cos (2 x - \frac{π}{4}) = \frac{2}{2}

sin (5 t) - 1 = 0

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