What is the general solution for 3tan(x^3)cot(x)1=0 ?

The general solution for 3tan(x^3)cot(x)1=0 is x=\sqrt[3]{pin},x= pi/2+pin

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3tan(x^3)cot(x)1=0

3 tan (x^{3}) cot (x) 1 = 0

Degrees

x = 0^{\circ} + 83.91493 \dots^{\circ} n, x = 9 0^{\circ} + 18 0^{\circ} n

Solution steps

3 tan (x^{3}) cot (x) \cdot 1 = 0

Solving each part separately

tan (x^{3}) = 0 or cot (x) = 0

tan (x^{3}) = 0

General solutions for

tan (x^{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}

x^{3} = 0 + πn

x^{3} = 0 + πn

Solve

x^{3} = 0 + πn

0 + πn = πn

x^{3} = πn

For

x^{n} = f (a)

, n is odd, the solution is

cot (x) = 0 : x = \frac{π}{2} + πn

cot (x) = 0

General solutions for

cot (x) = 0

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}{2} + πn

x = \frac{π}{2} + πn

Combine all the solutions

x, sin (\frac{y}{x}) + cos (\frac{x}{y}) = 0

sin (2 t) cos (t) = 0, 0 \leq t \leq π

2 sin^{3} (x) = sin^{3} (x)

θ, y = 4 sin (θ)

- 3 (sin^{2} (θ) - cos^{2} (θ)) = 0

What is the general solution for 3tan(x^3)cot(x)1=0 ?
The general solution for 3tan(x^3)cot(x)1=0 is x=\sqrt[3]{pin},x= pi/2+pin