What is the general solution for -7tan(x)+sqrt(3)=-3(sqrt(3)+tan(x)) ?

The general solution for -7tan(x)+sqrt(3)=-3(sqrt(3)+tan(x)) is x= pi/3+pin

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-7tan(x)+sqrt(3)=-3(sqrt(3)+tan(x))

Solution

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

Solution

x = \frac{π}{3} + πn

Degrees

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

Solution steps

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

Solve by substitution

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

Let:

tan (x) = u

- 7 u + 3 = - 3 (3 + u)

- 7 u + 3 = - 3 (3 + u) : u = 3

- 7 u + 3 = - 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

- 7 u + 3 = - 33 - 3 u

Move

3

to the right side

- 7 u + 3 = - 33 - 3 u

Subtract

3

from both sides

- 7 u + 3 - 3 = - 33 - 3 u - 3

Simplify

- 7 u + 3 - 3 = - 33 - 3 u - 3

Simplify

- 7 u + 3 - 3 : - 7 u

- 7 u + 3 - 3

Add similar elements:

3 - 3 = 0

= - 7 u

Simplify

- 33 - 3 u - 3 : - 3 u - 43

- 33 - 3 u - 3

Group like terms

= - 3 u - 33 - 3

Add similar elements:

- 33 - 3 = - 43

= - 3 u - 43

- 7 u = - 3 u - 43

- 7 u = - 3 u - 43

- 7 u = - 3 u - 43

Move

3 u

to the left side

- 7 u = - 3 u - 43

Add

3 u

to both sides

- 7 u + 3 u = - 3 u - 43 + 3 u

Simplify

- 4 u = - 43

- 4 u = - 43

Divide both sides by

- 4

- 4 u = - 43

Divide both sides by

- 4

\frac{- 4 u}{- 4} = \frac{- 4 3}{- 4}

Simplify

\frac{- 4 u}{- 4} = \frac{- 4 3}{- 4}

Simplify

\frac{- 4 u}{- 4} : u

\frac{- 4 u}{- 4}

Apply the fraction rule:

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

= \frac{4 u}{4}

Divide the numbers:

\frac{4}{4} = 1

= u

Simplify

\frac{- 4 3}{- 4} : 3

\frac{- 4 3}{- 4}

Apply the fraction rule:

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

= \frac{4 3}{4}

Divide the numbers:

\frac{4}{4} = 1

= 3

u = 3

u = 3

u = 3

Substitute back

u = tan (x)

tan (x) = 3

tan (x) = 3

tan (x) = 3 : x = \frac{π}{3} + πn

tan (x) = 3

General solutions for

tan (x) = 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}{3} + πn

x = \frac{π}{3} + πn

Combine all the solutions

x = \frac{π}{3} + πn

Popular Examples

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4 sin (x) = 3 csc (x)

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Frequently Asked Questions (FAQ)

What is the general solution for -7tan(x)+sqrt(3)=-3(sqrt(3)+tan(x)) ?
The general solution for -7tan(x)+sqrt(3)=-3(sqrt(3)+tan(x)) is x= pi/3+pin