What is the general solution for 1+tan(x)=0 ?

The general solution for 1+tan(x)=0 is x=(3pi)/4+pin

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1+tan(x)=0

1 + tan (x) = 0

x = \frac{3 π}{4} + πn

Degrees

x = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

1 + tan (x) = 0

Move

1

to the right side

1 + tan (x) = 0

Subtract

1

from both sides

1 + tan (x) - 1 = 0 - 1

Simplify

tan (x) = - 1

tan (x) = - 1

General solutions for

tan (x) = - 1

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{3 π}{4} + πn

x = \frac{3 π}{4} + πn

tan^{2} (x) - 3 = 0

cos (x) = \frac{3}{2}

cos (16 5^{\circ})

csc (2 π)

sin (0)

What is the general solution for 1+tan(x)=0 ?
The general solution for 1+tan(x)=0 is x=(3pi)/4+pin