What is the general solution for -21tan(x)+3sqrt(3)=-3(sqrt(3)+tan(x)) ?

The general solution for -21tan(x)+3sqrt(3)=-3(sqrt(3)+tan(x)) is x= pi/6+pin

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-21tan(x)+3sqrt(3)=-3(sqrt(3)+tan(x))

Solution

- 21 tan (x) + 33 = - 3 (3 + tan (x))

Solution

x = \frac{π}{6} + πn

Degrees

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

Solution steps

- 21 tan (x) + 33 = - 3 (3 + tan (x))

Solve by substitution

- 21 tan (x) + 33 = - 3 (3 + tan (x))

Let:

tan (x) = u

- 21 u + 33 = - 3 (3 + u)

- 21 u + 33 = - 3 (3 + u) : u = \frac{3}{3}

- 21 u + 33 = - 3 (3 + u)

Expand

- 3 (3 + u) : - 33 - 3 u

- 3 (3 + u)

Apply the distributive law:

a (b + c) = ab + a c

a = - 3, b = 3, c = u

= - 33 + (- 3) u

Apply minus-plus rules

+ (- a) = - a

= - 33 - 3 u

- 21 u + 33 = - 33 - 3 u

Move

33

to the right side

- 21 u + 33 = - 33 - 3 u

Subtract

33

from both sides

- 21 u + 33 - 33 = - 33 - 3 u - 33

Simplify

- 21 u + 33 - 33 = - 33 - 3 u - 33

Simplify

- 21 u + 33 - 33 : - 21 u

- 21 u + 33 - 33

Add similar elements:

33 - 33 = 0

= - 21 u

Simplify

- 33 - 3 u - 33 : - 3 u - 63

- 33 - 3 u - 33

Group like terms

= - 3 u - 33 - 33

Add similar elements:

- 33 - 33 = - 63

= - 3 u - 63

- 21 u = - 3 u - 63

- 21 u = - 3 u - 63

- 21 u = - 3 u - 63

Move

3 u

to the left side

- 21 u = - 3 u - 63

Add

3 u

to both sides

- 21 u + 3 u = - 3 u - 63 + 3 u

Simplify

- 18 u = - 63

- 18 u = - 63

Divide both sides by

- 18

- 18 u = - 63

Divide both sides by

- 18

\frac{- 18 u}{- 18} = \frac{- 6 3}{- 18}

Simplify

\frac{- 18 u}{- 18} = \frac{- 6 3}{- 18}

Simplify

\frac{- 18 u}{- 18} : u

\frac{- 18 u}{- 18}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{18 u}{18}

Divide the numbers:

\frac{18}{18} = 1

= u

Simplify

\frac{- 6 3}{- 18} : \frac{3}{3}

\frac{- 6 3}{- 18}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{6 3}{18}

Cancel the common factor:

6

= \frac{3}{3}

u = \frac{3}{3}

u = \frac{3}{3}

u = \frac{3}{3}

Substitute back

u = tan (x)

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

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

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

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

Combine all the solutions

x = \frac{π}{6} + πn

Popular Examples

tan(y)=-1

tan (y) = - 1

2pi+6arccos(2-x)=0

2 π + 6 arccos (2 - x) = 0

tan(x)= 12/4

tan (x) = \frac{12}{4}

1-sqrt(2)cos(θ)=0

1 - 2 cos (θ) = 0

sqrt(3)tan(3x)-1=0,0<= x<= 2pi

3 tan (3 x) - 1 = 0, 0 \leq x \leq 2 π

Frequently Asked Questions (FAQ)

What is the general solution for -21tan(x)+3sqrt(3)=-3(sqrt(3)+tan(x)) ?
The general solution for -21tan(x)+3sqrt(3)=-3(sqrt(3)+tan(x)) is x= pi/6+pin