What is the general solution for (tan(x)+sqrt(3))(cos(x)+2)=0 ?

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

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(tan(x)+sqrt(3))(cos(x)+2)=0

(tan (x) + 3) (cos (x) + 2) = 0

x = \frac{2 π}{3} + πn

Degrees

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

Solution steps

(tan (x) + 3) (cos (x) + 2) = 0

Solving each part separately

tan (x) + 3 = 0 or cos (x) + 2 = 0

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

cos (x) + 2 = 0 :

No Solution

cos (x) + 2 = 0

Move

2

to the right side

cos (x) + 2 = 0

Subtract

2

from both sides

cos (x) + 2 - 2 = 0 - 2

Simplify

cos (x) = - 2

cos (x) = - 2

- 1 \leq cos (x) \leq 1

No Solution

Combine all the solutions

x = \frac{2 π}{3} + πn

x, cos (y) + sin (x) = 1

cot (x) + 5 csc (x) = 6

csc^{2} (x) = 1

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

4 cos^{3} (x) = 4 cos (x)

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