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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2+sqrt(3)tan(x)=3

2 + 3 tan (x) = 3

x = \frac{π}{6} + πn

Degrees

x = 3 0^{\circ} + 18 0^{\circ} n

Solution steps

2 + 3 tan (x) = 3

Move

2

to the right side

2 + 3 tan (x) = 3

Subtract

2

from both sides

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

Simplify

3 tan (x) = 1

3 tan (x) = 1

Divide both sides by

3

3 tan (x) = 1

Divide both sides by

3

\frac{3 tan ( x )}{3} = \frac{1}{3}

Simplify

\frac{3 tan ( x )}{3} = \frac{1}{3}

Simplify

\frac{3 tan ( x )}{3} : tan (x)

\frac{3 tan ( x )}{3}

Cancel the common factor:

3

= tan (x)

Simplify

\frac{1}{3} : \frac{3}{3}

\frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{3}{3}

tan (x) = \frac{3}{3}

tan (x) = \frac{3}{3}

tan (x) = \frac{3}{3}

General solutions for

tan (x) = \frac{3}{3}

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}{6} + πn

x = \frac{π}{6} + πn

(sin (x) - 4) (sin (x) - 1) = 0

tan (2 x) = 0.6

2 sin (3 θ) = - 1

2 + 2 cos (θ) = 2 - 2 cos (θ)

1 + 4 sin (x) = 0

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