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

The general solution for (tan(x)+3)(tan(x)+2)=0 is x=-1.24904…+pin,x=-1.10714…+pin

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

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

x = - 1.24904 \dots + πn, x = - 1.10714 \dots + πn

Degrees

x = - 71.56505 \dots^{\circ} + 18 0^{\circ} n, x = - 63.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

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

Solving each part separately

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

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

Apply trig inverse properties

tan (x) = - 3

General solutions for

tan (x) = - 3

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- 3) + πn

x = arctan (- 3) + πn

tan (x) + 2 = 0 : x = arctan (- 2) + πn

tan (x) + 2 = 0