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

The general solution for cot(x)(tan(x)+sqrt(3))=0 is x=(2pi)/3+pin

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cot(x)(tan(x)+sqrt(3))=0

cot (x) (tan (x) + 3) = 0

x = \frac{2 π}{3} + πn

Degrees

x = 12 0^{\circ} + 18 0^{\circ} n

Solution steps

cot (x) (tan (x) + 3) = 0

Solving each part separately

cot (x) = 0 or tan (x) + 3 = 0

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

tan (x) + 3 = 0 : x = \frac{2 π}{3} + πn

tan (x) + 3 = 0

Move

3

to the right side

tan (x) + 3 = 0

Subtract

3

from both sides

tan (x) + 3 - 3 = 0 - 3

Simplify

tan (x) = - 3

tan (x) = - 3

General solutions for

tan (x) = - 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{2 π}{3} + πn

x = \frac{2 π}{3} + πn

Combine all the solutions

x = \frac{π}{2} + πn, x = \frac{2 π}{3} + πn

Since the equation is undefined for:

\frac{π}{2} + πn

x = \frac{2 π}{3} + πn

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

- cos (x - π) = \frac{3}{2}

cos^{4} (x) = 8 cos^{4} (x) - 8 cos^{2} (x) + 1

sin^{2} (x + \frac{π}{2}) = \frac{3}{4}

sin (2 x - \frac{π}{6}) = \frac{1}{2}

What is the general solution for cot(x)(tan(x)+sqrt(3))=0 ?
The general solution for cot(x)(tan(x)+sqrt(3))=0 is x=(2pi)/3+pin