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

The general solution for 3tan(θ)-cot(θ)=0 is θ= pi/6+pin,θ=(5pi)/6+pin

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3tan(θ)-cot(θ)=0

3 tan (θ) - cot (θ) = 0

θ = \frac{π}{6} + πn, θ = \frac{5 π}{6} + πn

Solution steps

3 tan (θ) - cot (θ) = 0

Rewrite using trig identities

- cot (θ) + \frac{3}{cot ( θ )} = 0

Solve by substitution

cot (θ) = 3, cot (θ) = - 3

cot (θ) = 3 : θ = \frac{π}{6} + πn

cot (θ) = - 3 : θ = \frac{5 π}{6} + πn

Combine all the solutions

θ = \frac{π}{6} + πn, θ = \frac{5 π}{6} + πn

sin (\frac{1}{2} x + \frac{π}{6}) = \frac{3}{2}

6 sin (3 x) = 2

cos (x) \cdot sin (x) = 0

sin^{2} (θ) + 4 sin (θ) + 3 = 0

2 \cdot cos (x) = 0

What is the general solution for 3tan(θ)-cot(θ)=0 ?
The general solution for 3tan(θ)-cot(θ)=0 is θ= pi/6+pin,θ=(5pi)/6+pin