What is the general solution for 3tan(2x+1)=2 ?

The general solution for 3tan(2x+1)=2 is x=(0.58800…)/2+(pin)/2-1/2

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3tan(2x+1)=2

3 tan (2 x + 1) = 2

x = \frac{0.58800 \dots}{2} + \frac{πn}{2} - \frac{1}{2}

Degrees

x = - 11.80285 \dots^{\circ} + 9 0^{\circ} n

Solution steps

3 tan (2 x + 1) = 2

Divide both sides by

3

3 tan (2 x + 1) = 2

Divide both sides by

3

\frac{3 tan ( 2 x + 1 )}{3} = \frac{2}{3}

Simplify

tan (2 x + 1) = \frac{2}{3}

tan (2 x + 1) = \frac{2}{3}

Apply trig inverse properties

tan (2 x + 1) = \frac{2}{3}

General solutions for

tan (2 x + 1) = \frac{2}{3}

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

2 x + 1 = arctan (\frac{2}{3}) + πn

2 x + 1 = arctan (\frac{2}{3}) + πn

Solve

2 x + 1 = arctan (\frac{2}{3}) + πn : x = \frac{arctan ( \frac{2}{3} )}{2} + \frac{πn}{2} - \frac{1}{2}

2 x + 1 = arctan (\frac{2}{3}) + πn

Move

1

to the right side

2 x + 1 = arctan (\frac{2}{3}) + πn

Subtract

1

from both sides

2 x + 1 - 1 = arctan (\frac{2}{3}) + πn - 1

Simplify

2 x = arctan (\frac{2}{3}) + πn - 1

2 x = arctan (\frac{2}{3}) + πn - 1

Divide both sides by

2

2 x = arctan (\frac{2}{3}) + πn - 1

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( \frac{2}{3} )}{2} + \frac{πn}{2} - \frac{1}{2}

Simplify

x = \frac{arctan ( \frac{2}{3} )}{2} + \frac{πn}{2} - \frac{1}{2}

x = \frac{arctan ( \frac{2}{3} )}{2} + \frac{πn}{2} - \frac{1}{2}

x = \frac{arctan ( \frac{2}{3} )}{2} + \frac{πn}{2} - \frac{1}{2}

Show solutions in decimal form

x = \frac{0.58800 \dots}{2} + \frac{πn}{2} - \frac{1}{2}

What is the general solution for 3tan(2x+1)=2 ?
The general solution for 3tan(2x+1)=2 is x=(0.58800…)/2+(pin)/2-1/2