What is the general solution for tan(3x)(tan(x)-1)=0 ?

The general solution for tan(3x)(tan(x)-1)=0 is x=(pin)/3 ,x= pi/4+pin

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tan(3x)(tan(x)-1)=0

tan (3 x) (tan (x) - 1) = 0

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

Degrees

x = 0^{\circ} + 6 0^{\circ} n, x = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

tan (3 x) (tan (x) - 1) = 0

Solving each part separately

tan (3 x) = 0 or tan (x) - 1 = 0

tan (3 x) = 0 : x = \frac{πn}{3}

tan (3 x) = 0

General solutions for

tan (3 x) = 0

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

3 x = 0 + πn

3 x = 0 + πn

Solve

3 x = 0 + πn : x = \frac{πn}{3}

3 x = 0 + πn

0 + πn = πn

3 x = πn

Divide both sides by

3

3 x = πn

Divide both sides by

3

\frac{3 x}{3} = \frac{πn}{3}

Simplify

x = \frac{πn}{3}

x = \frac{πn}{3}

x = \frac{πn}{3}

tan (x) - 1 = 0 : x = \frac{π}{4} + πn

tan (x) - 1 = 0

Move

1

to the right side

tan (x) - 1 = 0

Add

1

to both sides

tan (x) - 1 + 1 = 0 + 1

Simplify

tan (x) = 1

tan (x) = 1

General solutions for

tan (x) = 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

Combine all the solutions

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

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

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

2 sin (2 x) = 1, 0 \leq x \leq 2 π

sin (θ) = \frac{1}{4}

2 sin (θ) + 3 = 2

What is the general solution for tan(3x)(tan(x)-1)=0 ?
The general solution for tan(3x)(tan(x)-1)=0 is x=(pin)/3 ,x= pi/4+pin