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

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

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cot(pi/3)=tan(x)

cot (\frac{π}{3}) = tan (x)

x = \frac{π}{6} + πn

Degrees

x = 3 0^{\circ} + 18 0^{\circ} n

Solution steps

cot (\frac{π}{3}) = tan (x)

cot (\frac{π}{3}) = \frac{3}{3}

cot (\frac{π}{3})

Use the following trivial identity:

cot (\frac{π}{3}) = \frac{3}{3}

cot (\frac{π}{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

= \frac{3}{3}

= \frac{3}{3}

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

Switch sides

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

General solutions for

tan (x) = \frac{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}{6} + πn

x = \frac{π}{6} + πn

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