What is the general solution for 3(tan(x))+sqrt(12)=sqrt(3) ?

The general solution for 3(tan(x))+sqrt(12)=sqrt(3) is x=(5pi)/6+pin

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Popular >

3(tan(x))+sqrt(12)=sqrt(3)

Solution

3 (tan (x)) + 12 = 3

Solution

x = \frac{5 π}{6} + πn

Degrees

x = 15 0^{\circ} + 18 0^{\circ} n

Solution steps

3 (tan (x)) + 12 = 3

12 = 23

12

Prime factorization of

12 : 2^{2} \cdot 3

12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3

= 2^{2} \cdot 3

= 2^{2} \cdot 3

Apply radical rule:

= 3 2^{2}

Apply radical rule:

2^{2} = 2

= 23

3 tan (x) + 23 = 3

Move

23

to the right side

3 tan (x) + 23 = 3

Subtract

23

from both sides

3 tan (x) + 23 - 23 = 3 - 23

Simplify

3 tan (x) + 23 - 23 = 3 - 23

Simplify

3 tan (x) + 23 - 23 : 3 tan (x)

3 tan (x) + 23 - 23

Add similar elements:

23 - 23 = 0

= 3 tan (x)

Simplify

3 - 23 : - 3

3 - 23

Add similar elements:

3 - 23 = - 3

= - 3

3 tan (x) = - 3

3 tan (x) = - 3

3 tan (x) = - 3

Divide both sides by

3

3 tan (x) = - 3

Divide both sides by

3

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

Simplify

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{5 π}{6} + πn

x = \frac{5 π}{6} + πn

Popular Examples

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

tan (3 x) - 3 = 0

3sin(x)-2=5sin(x)-1

3 sin (x) - 2 = 5 sin (x) - 1

1+cos(θ)=3cos(θ)

1 + cos (θ) = 3 cos (θ)

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

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

tan(x)=sqrt(1/3)

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

Frequently Asked Questions (FAQ)

What is the general solution for 3(tan(x))+sqrt(12)=sqrt(3) ?
The general solution for 3(tan(x))+sqrt(12)=sqrt(3) is x=(5pi)/6+pin