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

csc (x) + 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

cos (x) - sin (x) = 0.5

sin (x + π) - sin (x) + 3 = 0

csc (x) = 1.5

tan (t) = 0

cos (\frac{θ}{2}) = \frac{1}{2}

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