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

The general solution for cot^2(x)=1-csc(x) is x= pi/2+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

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

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

x = \frac{π}{2} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

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

Subtract

1 - csc (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

csc (x) = 1, csc (x) = - 2

csc (x) = 1 : x = \frac{π}{2} + 2 πn

csc (x) = - 2 : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

2 sin^{2} (θ) + 9 sin (θ) - 5 = 0

sin (x) tan (x) - sin (x) = 0

sinh (x) = \frac{15}{8}

(2 cos (x) - 1) (2 sin (x) - 3) = 0

sin (α) + cos (α) = \frac{1}{2}

What is the general solution for cot^2(x)=1-csc(x) ?
The general solution for cot^2(x)=1-csc(x) is x= pi/2+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin