What is the general solution for 3tan(x)=tan(2x) ?

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

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3tan(x)=tan(2x)

3 tan (x) = tan (2 x)

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

Solution steps

3 tan (x) = tan (2 x)

Subtract

tan (2 x)

from both sides

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

Rewrite using trig identities

\frac{tan ( x ) - 3 tan ^{3} ( x )}{1 - tan ^{2} ( x )} = 0

Solve by substitution

tan (x) = 0, tan (x) = - \frac{3}{3}, tan (x) = \frac{3}{3}

tan (x) = 0 : x = πn

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

tan (x) = \frac{3}{3} : x = \frac{π}{6} + πn

Combine all the solutions

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

cos (4 x) + sin (6 x) = 0

- 15.44 = - 2 sin (- 3 θ + 300)

sin (x) = - cos (3 4^{\circ})

2 sin^{2} (x) = cos^{3} (x) tan (x)

tan (x - 1 0^{\circ}) cot (2 0^{\circ} - x) = 1

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