What is the general solution for tan(3x-pi)=1 ?

The general solution for tan(3x-pi)=1 is x= pi/3+pi/(12)+(pin)/3

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tan(3x-pi)=1

tan (3 x - π) = 1

x = \frac{π}{3} + \frac{π}{12} + \frac{πn}{3}

Degrees

x = 7 5^{\circ} + 6 0^{\circ} n

Solution steps

tan (3 x - π) = 1

General solutions for

tan (3 x - π) = 1

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}

3 x - π = \frac{π}{4} + πn

3 x - π = \frac{π}{4} + πn

Solve

3 x - π = \frac{π}{4} + πn : x = \frac{π}{3} + \frac{π}{12} + \frac{πn}{3}

3 x - π = \frac{π}{4} + πn

Move

π

to the right side

3 x - π = \frac{π}{4} + πn

Add

π

to both sides

3 x - π + π = \frac{π}{4} + πn + π

Simplify

3 x = \frac{π}{4} + πn + π

3 x = \frac{π}{4} + πn + π

Divide both sides by

3

3 x = \frac{π}{4} + πn + π

Divide both sides by

3

\frac{3 x}{3} = \frac{\frac{π}{4}}{3} + \frac{πn}{3} + \frac{π}{3}

Simplify

\frac{3 x}{3} = \frac{\frac{π}{4}}{3} + \frac{πn}{3} + \frac{π}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{π}{4}}{3} + \frac{πn}{3} + \frac{π}{3} : \frac{π}{3} + \frac{π}{12} + \frac{πn}{3}

\frac{\frac{π}{4}}{3} + \frac{πn}{3} + \frac{π}{3}

Group like terms

= \frac{π}{3} + \frac{πn}{3} + \frac{\frac{π}{4}}{3}

\frac{\frac{π}{4}}{3} = \frac{π}{12}

\frac{\frac{π}{4}}{3}

Apply the fraction rule:

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

= \frac{π}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{π}{12}

= \frac{π}{3} + \frac{πn}{3} + \frac{π}{12}

Group like terms

= \frac{π}{3} + \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{3} + \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{3} + \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{3} + \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{3} + \frac{π}{12} + \frac{πn}{3}

sin (2 x) cos (x) + cos (2 x) sin (x) = 1

sin (2 x) cos (x) + cos (2 x) sin (x) = 0

- 10 sin (θ) + 2 = 2

cot (u) - csc (u) = \frac{sin ( u )}{1 + cos ( u )}

sin (x) = \frac{5}{3}

What is the general solution for tan(3x-pi)=1 ?
The general solution for tan(3x-pi)=1 is x= pi/3+pi/(12)+(pin)/3