What is the general solution for 3-2cot^2(x)=-cot^2(x) ?

The general solution for 3-2cot^2(x)=-cot^2(x) is x= pi/6+pin,x=(5pi)/6+pin

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3-2cot^2(x)=-cot^2(x)

3 - 2 cot^{2} (x) = - cot^{2} (x)

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

Solution steps

3 - 2 cot^{2} (x) = - cot^{2} (x)

Solve by substitution

cot (x) = 3, cot (x) = - 3

cot (x) = 3 : x = \frac{π}{6} + πn

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

Combine all the solutions

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

2 cos (t) + 1 = 0

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

tan^{2} (θ) = - tan (θ)

sec (θ) = - \frac{2}{3}

tan (θ) = \frac{8}{12}

What is the general solution for 3-2cot^2(x)=-cot^2(x) ?
The general solution for 3-2cot^2(x)=-cot^2(x) is x= pi/6+pin,x=(5pi)/6+pin