What is the general solution for 3cot^2(3x)-9=0 ?

The general solution for 3cot^2(3x)-9=0 is x= pi/(18)+(pin)/3 ,x=(5pi}{18}+\frac{pin)/3

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3cot^2(3x)-9=0

3 cot^{2} (3 x) - 9 = 0

x = \frac{π}{18} + \frac{πn}{3}, x = \frac{5 π}{18} + \frac{πn}{3}

Solution steps

3 cot^{2} (3 x) - 9 = 0

Solve by substitution

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

cot (3 x) = 3 : x = \frac{π}{18} + \frac{πn}{3}

cot (3 x) = - 3 : x = \frac{5 π}{18} + \frac{πn}{3}

Combine all the solutions

x = \frac{π}{18} + \frac{πn}{3}, x = \frac{5 π}{18} + \frac{πn}{3}

0 = cos (5 θ)

cos (x) = - \frac{1}{2}, 0 \leq x < 2 π

tan (x) = - \frac{5}{12}

cos (x) = 0.63

cos (x) = 0.58

What is the general solution for 3cot^2(3x)-9=0 ?
The general solution for 3cot^2(3x)-9=0 is x= pi/(18)+(pin)/3 ,x=(5pi}{18}+\frac{pin)/3