What is the general solution for 3tan(x)=cot(x) ?

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

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3tan(x)=cot(x)

3 tan (x) = cot (x)

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

Solution steps

3 tan (x) = cot (x)

Subtract

cot (x)

from both sides

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

Rewrite using trig identities

- cot (x) + \frac{3}{cot ( x )} = 0

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

cos (θ) = \frac{7}{25}

2 tan^{2} (θ) sin (θ) - tan^{2} (θ) = 0

sin^{2} (x) = - 3 sin (x) + 4

tan^{2} (x) csc (x) = tan^{2} (x)

12.3 = 2.3 sin (24 x) + 14.1

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