What is the general solution for csc^2(θ)=3cot(θ)+5 ?

The general solution for csc^2(θ)=3cot(θ)+5 is θ=0.24497…+pin,θ=(3pi)/4+pin

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csc^2(θ)=3cot(θ)+5

csc^{2} (θ) = 3 cot (θ) + 5

θ = 0.24497 \dots + πn, θ = \frac{3 π}{4} + πn

Solution steps

csc^{2} (θ) = 3 cot (θ) + 5

Subtract

3 cot (θ) + 5

from both sides

csc^{2} (θ) - 3 cot (θ) - 5 = 0

Rewrite using trig identities

- 4 + cot^{2} (θ) - 3 cot (θ) = 0

Solve by substitution

cot (θ) = 4, cot (θ) = - 1

cot (θ) = 4 : θ = arccot (4) + πn

cot (θ) = - 1 : θ = \frac{3 π}{4} + πn

Combine all the solutions

θ = arccot (4) + πn, θ = \frac{3 π}{4} + πn

Show solutions in decimal form

θ = 0.24497 \dots + πn, θ = \frac{3 π}{4} + πn

sin^{2} (x) - 2 sin (x) = 0, 0 \leq x < 2 π

cos (2 x) = \frac{( 5 k - 8 )}{5}

x, - f = sin (x)

\frac{1}{2} cos (2 x - \frac{π}{3}) + 4 = 0

sin (B) = \frac{16 sin ( 10 4 ^{\circ} )}{25}

What is the general solution for csc^2(θ)=3cot(θ)+5 ?
The general solution for csc^2(θ)=3cot(θ)+5 is θ=0.24497…+pin,θ=(3pi)/4+pin