What is the general solution for 6tan(x)+1=4tan(x)+3 ?

The general solution for 6tan(x)+1=4tan(x)+3 is x= pi/4+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometry >

6tan(x)+1=4tan(x)+3

Solution

6 tan (x) + 1 = 4 tan (x) + 3

Solution

x = \frac{π}{4} + πn

Degrees

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

Solution steps

6 tan (x) + 1 = 4 tan (x) + 3

Solve by substitution

6 tan (x) + 1 = 4 tan (x) + 3

Let:

tan (x) = u

6 u + 1 = 4 u + 3

6 u + 1 = 4 u + 3 : u = 1

6 u + 1 = 4 u + 3

Move

1

to the right side

6 u + 1 = 4 u + 3

Subtract

1

from both sides

6 u + 1 - 1 = 4 u + 3 - 1

Simplify

6 u = 4 u + 2

6 u = 4 u + 2

Move

4 u

to the left side

6 u = 4 u + 2

Subtract

4 u

from both sides

6 u - 4 u = 4 u + 2 - 4 u

Simplify

2 u = 2

2 u = 2

Divide both sides by

2

2 u = 2

Divide both sides by

2

\frac{2 u}{2} = \frac{2}{2}

Simplify

u = 1

u = 1

Substitute back

u = tan (x)

tan (x) = 1

tan (x) = 1

tan (x) = 1 : x = \frac{π}{4} + πn

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{π}{4} + πn

Graph

Popular Examples

cos(x)=(-sqrt(5))/5

cos(A)=(4^2+(5.1)^2-3^2)/(2-4*5.1)

cos(a)= 5/4

1-2sin^2(x)= 1/2

2cos(2θ+10)=1

Frequently Asked Questions (FAQ)

What is the general solution for 6tan(x)+1=4tan(x)+3 ?
The general solution for 6tan(x)+1=4tan(x)+3 is x= pi/4+pin