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

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

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tan(x+pi/3)=sqrt(3)

tan (x + \frac{π}{3}) = 3

x = πn

Degrees

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

Solution steps

tan (x + \frac{π}{3}) = 3

General solutions for

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

x + \frac{π}{3} = \frac{π}{3} + πn

Solve

x + \frac{π}{3} = \frac{π}{3} + πn : x = πn

x + \frac{π}{3} = \frac{π}{3} + πn

Subtract

\frac{π}{3}

from both sides

x + \frac{π}{3} - \frac{π}{3} = \frac{π}{3} + πn - \frac{π}{3}

Simplify

x = πn

x = πn

16 sin^{2} (x) = 1

x, - 1 \cdot \frac{cos ( x )}{sin ( x )} = 0

8 cos (θ) - 4 = 0

2 (1 + cos (θ)) = 0

0 = cos (π x) \cdot π + sin (π x) π

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