What is the general solution for 9tan(3x)=9 ?

The general solution for 9tan(3x)=9 is x= pi/(12)+(pin)/3

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9tan(3x)=9

9 tan (3 x) = 9

x = \frac{π}{12} + \frac{πn}{3}

Degrees

x = 1 5^{\circ} + 6 0^{\circ} n

Solution steps

9 tan (3 x) = 9

Divide both sides by

9

9 tan (3 x) = 9

Divide both sides by

9

\frac{9 tan ( 3 x )}{9} = \frac{9}{9}

Simplify

tan (3 x) = 1

tan (3 x) = 1

General solutions for

tan (3 x) = 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 = \frac{π}{4} + πn

3 x = \frac{π}{4} + πn

Solve

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

3 x = \frac{π}{4} + πn

Divide both sides by

3

3 x = \frac{π}{4} + πn

Divide both sides by

3

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

Simplify

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

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

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

sin (θ) = \frac{40}{41}

cos (2 x) - sin^{2} (x) = \frac{1}{4}

sec (θ) csc (θ) + 2 csc (θ) = 0

2 sin^{2} (θ) - sin (θ) - 1 = 0, 0 \leq θ \leq 2 π

sin (3 θ) = \frac{2}{2}

What is the general solution for 9tan(3x)=9 ?
The general solution for 9tan(3x)=9 is x= pi/(12)+(pin)/3