What is the general solution for 6tan(θ)-2cot(θ)=0 ?

The general solution for 6tan(θ)-2cot(θ)=0 is θ= pi/6+pin,θ=(5pi)/6+pin

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6tan(θ)-2cot(θ)=0

6 tan (θ) - 2 cot (θ) = 0

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

Solution steps

6 tan (θ) - 2 cot (θ) = 0

Rewrite using trig identities

\frac{6}{cot ( θ )} - 2 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

- 2 sin^{2} (x) = 7 cos (x) + 2

2 sin^{2} (θ) + sin (θ) = 0, 0 \leq θ < 2 π

cos (x) (2 cos (x) + 1) = 3

3 + cot (x) = 0

sin (θ) = - \frac{5}{8}

What is the general solution for 6tan(θ)-2cot(θ)=0 ?
The general solution for 6tan(θ)-2cot(θ)=0 is θ= pi/6+pin,θ=(5pi)/6+pin