What is the general solution for tan(x)(cot(x)-(sqrt(3))/3)=0 ?

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

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tan(x)(cot(x)-(sqrt(3))/3)=0

tan (x) (cot (x) - \frac{3}{3}) = 0

x = \frac{π}{3} + πn

Degrees

x = 6 0^{\circ} + 18 0^{\circ} n

Solution steps

tan (x) (cot (x) - \frac{3}{3}) = 0

Solving each part separately

tan (x) = 0 or cot (x) - \frac{3}{3} = 0

tan (x) = 0 : x = πn

tan (x) = 0

General solutions for

tan (x) = 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}

x = 0 + πn

x = 0 + πn

Solve

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

cot (x) - \frac{3}{3} = 0 : x = \frac{π}{3} + πn

cot (x) - \frac{3}{3} = 0

Move

\frac{3}{3}

to the right side

cot (x) - \frac{3}{3} = 0

Add

\frac{3}{3}

to both sides

cot (x) - \frac{3}{3} + \frac{3}{3} = 0 + \frac{3}{3}

Simplify

cot (x) = \frac{3}{3}

cot (x) = \frac{3}{3}

General solutions for

cot (x) = \frac{3}{3}

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{3} + πn

x = \frac{π}{3} + πn

Combine all the solutions

x = πn, x = \frac{π}{3} + πn

Since the equation is undefined for:

πn

x = \frac{π}{3} + πn

24 sin^{2} (x) = 24 - 12 cos (x)

3 tan (x) = 1

2 cos^{2} (t) + 3 cos (t) + 1 = 0

cos (x) = - \frac{1}{5}

tan (\frac{x}{2}) = sin (x)

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