What is the general solution for tan(θ)-3cot(θ)=0 ?

The general solution for tan(θ)-3cot(θ)=0 is θ=1.04719…+pin,θ=2.09439…+pin

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tan(θ)-3cot(θ)=0

tan (θ) - 3 cot (θ) = 0

θ = 1.04719 \dots + πn, θ = 2.09439 \dots + πn

Solution steps

tan (θ) - 3 cot (θ) = 0

Rewrite using trig identities

\frac{1}{cot ( θ )} - 3 cot (θ) = 0

Solve by substitution

cot (θ) = \frac{1}{3}, cot (θ) = - \frac{1}{3}

cot (θ) = \frac{1}{3} : θ = arccot (\frac{1}{3}) + πn

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

Combine all the solutions

θ = arccot (\frac{1}{3}) + πn, θ = arccot (- \frac{1}{3}) + πn

Show solutions in decimal form

θ = 1.04719 \dots + πn, θ = 2.09439 \dots + πn

cot (- \frac{π}{2})

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

sin (1 5^{\circ})

sec (12 0^{\circ})

csc (9 0^{\circ})

What is the general solution for tan(θ)-3cot(θ)=0 ?
The general solution for tan(θ)-3cot(θ)=0 is θ=1.04719…+pin,θ=2.09439…+pin