What is the general solution for tan(x+pi/6)= 2/3 ?

The general solution for tan(x+pi/6)= 2/3 is x=0.58800…+pin-pi/6

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tan(x+pi/6)= 2/3

tan (x + \frac{π}{6}) = \frac{2}{3}

x = 0.58800 \dots + πn - \frac{π}{6}

Degrees

x = 3.69006 \dots^{\circ} + 18 0^{\circ} n

Solution steps

tan (x + \frac{π}{6}) = \frac{2}{3}

Apply trig inverse properties

tan (x + \frac{π}{6}) = \frac{2}{3}

General solutions for

tan (x + \frac{π}{6}) = \frac{2}{3}

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

x + \frac{π}{6} = arctan (\frac{2}{3}) + πn

x + \frac{π}{6} = arctan (\frac{2}{3}) + πn

Solve

x + \frac{π}{6} = arctan (\frac{2}{3}) + πn : x = arctan (\frac{2}{3}) + πn - \frac{π}{6}

x + \frac{π}{6} = arctan (\frac{2}{3}) + πn

Move

\frac{π}{6}

to the right side

x + \frac{π}{6} = arctan (\frac{2}{3}) + πn

Subtract

\frac{π}{6}

from both sides

x + \frac{π}{6} - \frac{π}{6} = arctan (\frac{2}{3}) + πn - \frac{π}{6}

Simplify

x = arctan (\frac{2}{3}) + πn - \frac{π}{6}

x = arctan (\frac{2}{3}) + πn - \frac{π}{6}

x = arctan (\frac{2}{3}) + πn - \frac{π}{6}

Show solutions in decimal form

x = 0.58800 \dots + πn - \frac{π}{6}

4 cos^{2} (x) + 4 sin (x) - 5 = 0

sin (\frac{a x}{2}) = 0

\frac{3}{3} = - \frac{1}{3} \cdot tan (θ)

tan (x + \frac{π}{3}) = 3

16 sin^{2} (x) = 1

What is the general solution for tan(x+pi/6)= 2/3 ?
The general solution for tan(x+pi/6)= 2/3 is x=0.58800…+pin-pi/6