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

The general solution for cot^2(3x)-tan^2(3x)=0 is x= pi/(12)+(pin)/3 ,x= pi/4+(pin)/3

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

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

x = \frac{π}{12} + \frac{πn}{3}, x = \frac{π}{4} + \frac{πn}{3}

Solution steps

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

Factor

cot^{2} (3 x) - tan^{2} (3 x) : (cot (3 x) + tan (3 x)) (cot (3 x) - tan (3 x))

(cot (3 x) + tan (3 x)) (cot (3 x) - tan (3 x)) = 0

Solving each part separately

cot (3 x) + tan (3 x) = 0 or cot (3 x) - tan (3 x) = 0

cot (3 x) + tan (3 x) = 0 :

No Solution

cot (3 x) - tan (3 x) = 0 : x = \frac{π}{12} + \frac{πn}{3}, x = \frac{π}{4} + \frac{πn}{3}

Combine all the solutions

x = \frac{π}{12} + \frac{πn}{3}, x = \frac{π}{4} + \frac{πn}{3}

x, cos (x) = 10

3 cos (θ) = 2, 1

3 csc (x) - 7 = 0

tan (2 θ) = 0.6583

sin (x) = \frac{8}{12.8}

What is the general solution for cot^2(3x)-tan^2(3x)=0 ?
The general solution for cot^2(3x)-tan^2(3x)=0 is x= pi/(12)+(pin)/3 ,x= pi/4+(pin)/3