What is the general solution for cot^2(θ)+csc(θ)=1,0<= θ<2pi ?

The general solution for cot^2(θ)+csc(θ)=1,0<= θ<2pi is θ= pi/2 ,θ=(7pi)/6 ,θ=(11pi)/6

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cot^2(θ)+csc(θ)=1,0<= θ<2pi

cot^{2} (θ) + csc (θ) = 1, 0 \leq θ < 2 π

θ = \frac{π}{2}, θ = \frac{7 π}{6}, θ = \frac{11 π}{6}

Solution steps

cot^{2} (θ) + csc (θ) = 1, 0 \leq θ < 2 π

Subtract

1

from both sides

cot^{2} (θ) + csc (θ) - 1 = 0

Rewrite using trig identities

- 2 + csc (θ) + csc^{2} (θ) = 0

Solve by substitution

csc (θ) = 1, csc (θ) = - 2

csc (θ) = 1, 0 \leq θ < 2 π : θ = \frac{π}{2}

csc (θ) = - 2, 0 \leq θ < 2 π : θ = \frac{7 π}{6}, θ = \frac{11 π}{6}

Combine all the solutions

θ = \frac{π}{2}, θ = \frac{7 π}{6}, θ = \frac{11 π}{6}

tan (x) = \frac{sec ( x )}{cos ( x )}

sin (x) = - 0.707

2 sin^{2} (x) + 5 sin (x) = 0

cos (2 x) - 7 cos (x) - 3 = 0

tan^{2} (4 5^{\circ} - \frac{x}{3}) = 0.58

What is the general solution for cot^2(θ)+csc(θ)=1,0<= θ<2pi ?
The general solution for cot^2(θ)+csc(θ)=1,0<= θ<2pi is θ= pi/2 ,θ=(7pi)/6 ,θ=(11pi)/6