What is the general solution for tan(6x)-3tan(3x)=0 ?

The general solution for tan(6x)-3tan(3x)=0 is x=(pin)/3 ,x=(5pi+6pin)/(18),x=(pi+6pin)/(18)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(6x)-3tan(3x)=0

tan (6 x) - 3 tan (3 x) = 0

x = \frac{πn}{3}, x = \frac{5 π + 6 πn}{18}, x = \frac{π + 6 πn}{18}

Solution steps

tan (6 x) - 3 tan (3 x) = 0

Let:

u = 3 x

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

Rewrite using trig identities

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

Solve by substitution

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

tan (u) = 0 : u = πn

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

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

Combine all the solutions

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

Substitute back

u = 3 x

3 x = πn : x = \frac{πn}{3}

3 x = \frac{5 π}{6} + πn : x = \frac{5 π + 6 πn}{18}

3 x = \frac{π}{6} + πn : x = \frac{π + 6 πn}{18}

x = \frac{πn}{3}, x = \frac{5 π + 6 πn}{18}, x = \frac{π + 6 πn}{18}

sin (a) = \frac{2}{5}

cos^{2} (θ) - cos (θ) - 1 = 0

3 cot^{2} (x) - 4 csc (x) = 1

\frac{18 cos ( 2 θ ) + 27 cos ( θ )}{2} = 0

cos (x) = sin (2 x) + cos (3 x)

What is the general solution for tan(6x)-3tan(3x)=0 ?
The general solution for tan(6x)-3tan(3x)=0 is x=(pin)/3 ,x=(5pi+6pin)/(18),x=(pi+6pin)/(18)