What is the general solution for tan(2x+pi/3)=0 ?

The general solution for tan(2x+pi/3)=0 is x=(pin)/2-pi/6

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tan(2x+pi/3)=0

tan (2 x + \frac{π}{3}) = 0

x = \frac{πn}{2} - \frac{π}{6}

Degrees

x = - 3 0^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 x + \frac{π}{3}) = 0

General solutions for

tan (2 x + \frac{π}{3}) = 0

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}

2 x + \frac{π}{3} = 0 + πn

2 x + \frac{π}{3} = 0 + πn

Solve

2 x + \frac{π}{3} = 0 + πn : x = \frac{πn}{2} - \frac{π}{6}

2 x + \frac{π}{3} = 0 + πn

0 + πn = πn

2 x + \frac{π}{3} = πn

Move

\frac{π}{3}

to the right side

2 x + \frac{π}{3} = πn

Subtract

\frac{π}{3}

from both sides

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

Simplify

2 x = πn - \frac{π}{3}

2 x = πn - \frac{π}{3}

Divide both sides by

2

2 x = πn - \frac{π}{3}

Divide both sides by

2

\frac{2 x}{2} = \frac{πn}{2} - \frac{\frac{π}{3}}{2}

Simplify

\frac{2 x}{2} = \frac{πn}{2} - \frac{\frac{π}{3}}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{πn}{2} - \frac{\frac{π}{3}}{2} : \frac{πn}{2} - \frac{π}{6}

\frac{πn}{2} - \frac{\frac{π}{3}}{2}

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

Apply the fraction rule:

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

= \frac{π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{π}{6}

= \frac{πn}{2} - \frac{π}{6}

x = \frac{πn}{2} - \frac{π}{6}

x = \frac{πn}{2} - \frac{π}{6}

x = \frac{πn}{2} - \frac{π}{6}

x = \frac{πn}{2} - \frac{π}{6}

18 cos^{2} (x) = 9

\frac{1}{cot ( x )} - \frac{sec ( x )}{csc ( x )} = cos (x)

10 sin (x) + 10 cos^{2} (x) = 10, 0 \leq x < 2 π

sin (x) = 1, 2 π \leq x \leq 4 π

cos (a) = 1

What is the general solution for tan(2x+pi/3)=0 ?
The general solution for tan(2x+pi/3)=0 is x=(pin)/2-pi/6