What is the general solution for csc^2(θ)=2cot(θ) ?

The general solution for csc^2(θ)=2cot(θ) is θ= pi/4+pin

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csc^2(θ)=2cot(θ)

csc^{2} (θ) = 2 cot (θ)

θ = \frac{π}{4} + πn

Solution steps

csc^{2} (θ) = 2 cot (θ)

Subtract

2 cot (θ)

from both sides

csc^{2} (θ) - 2 cot (θ) = 0

Rewrite using trig identities

1 + cot^{2} (θ) - 2 cot (θ) = 0

Solve by substitution

cot (θ) = 1

cot (θ) = 1 : θ = \frac{π}{4} + πn

Combine all the solutions

θ = \frac{π}{4} + πn

tan (2 x) = + \frac{8}{15}

sin (θ) = \frac{7}{25}, cos (\frac{θ}{2}), 0^{\circ} < θ < 9 0^{\circ}

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

2 cos^{4} (θ) - 3 cos^{2} (θ) + 1 = 0

2 cos^{2} (θ) + 7 cos (θ) - 4 = 0

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