What is the general solution for 3(tan(x)-2)=2tan(-7) ?

The general solution for 3(tan(x)-2)=2tan(-7) is No Solution for x\in\mathbb{R}

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3(tan(x)-2)=2tan(-7)

3 (tan (x) - 2) = 2 tan (- 7)

No Solution for x \in R

Solution steps

3 (tan (x) - 2) = 2 tan (- 7)

tan (- 7) = - tan (7)

tan (- 7)

Use the following property:

tan (- x) = - tan (x)

tan (- 7) = - tan (7)

= - tan (7)

3 (tan (x) - 2) = 2 - tan (7)

Divide both sides by

3

3 (tan (x) - 2) = 2 - tan (7)

Divide both sides by

3

\frac{3 ( tan ( x ) - 2 )}{3} = \frac{2}{3} - \frac{tan ( 7 )}{3}

Simplify

\frac{3 ( tan ( x ) - 2 )}{3} = \frac{2}{3} - \frac{tan ( 7 )}{3}

Simplify

\frac{3 ( tan ( x ) - 2 )}{3} : tan (x) - 2

\frac{3 ( tan ( x ) - 2 )}{3}

Divide the numbers:

\frac{3}{3} = 1

= tan (x) - 2

Simplify

\frac{2}{3} - \frac{tan ( 7 )}{3} : \frac{2 - tan ( 7 )}{3}

\frac{2}{3} - \frac{tan ( 7 )}{3}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 - tan ( 7 )}{3}

tan (x) - 2 = \frac{2 - tan ( 7 )}{3}

tan (x) - 2 = \frac{2 - tan ( 7 )}{3}

tan (x) - 2 = \frac{2 - tan ( 7 )}{3}

Move

2

to the right side

tan (x) - 2 = \frac{2 - tan ( 7 )}{3}

Add

2

to both sides

tan (x) - 2 + 2 = \frac{2 - tan ( 7 )}{3} + 2

Simplify

tan (x) = \frac{2 - tan ( 7 )}{3} + 2

tan (x) = \frac{2 - tan ( 7 )}{3} + 2

Apply trig inverse properties

tan (x) = \frac{2 - tan ( 7 )}{3} + 2

General solutions for

tan (x) = \frac{2 - tan ( 7 )}{3} + 2

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (\frac{2 - tan ( 7 )}{3} + 2) + πn

x = arctan (\frac{2 - tan ( 7 )}{3} + 2) + πn

Since the equation is undefined for:

arctan (\frac{2 - tan ( 7 )}{3} + 2) + πn

No Solution for x \in R

6 sec (θ) + 7 = 0

cos (2 x) - sin (2 x) - 1 = 0

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x, 3 tan^{2} (x) - 1 = 0

cos (4 x) - 3 cos (2 x) - 1 = 0

What is the general solution for 3(tan(x)-2)=2tan(-7) ?
The general solution for 3(tan(x)-2)=2tan(-7) is No Solution for x\in\mathbb{R}