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

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

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

\frac{tan ( x )}{1 + tan ( x )} = 0

x = πn

Degrees

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

Solution steps

\frac{tan ( x )}{1 + tan ( x )} = 0

Solve by substitution

\frac{tan ( x )}{1 + tan ( x )} = 0

Let:

tan (x) = u

\frac{u}{1 + u} = 0

\frac{u}{1 + u} = 0 : u = 0

\frac{u}{1 + u} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

u = 0

Verify Solutions

Find undefined (singularity) points:

u = - 1

Take the denominator(s) of

\frac{u}{1 + u}

and compare to zero

Solve

1 + u = 0 : u = - 1

1 + u = 0

Move

1

to the right side

1 + u = 0

Subtract

1

from both sides

1 + u - 1 = 0 - 1

Simplify

u = - 1

u = - 1

The following points are undefined

u = - 1

Combine undefined points with solutions:

u = 0

Substitute back

u = tan (x)

tan (x) = 0

tan (x) = 0

tan (x) = 0 : x = πn

tan (x) = 0

General solutions for

tan (x) = 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 = 0 + πn

x = 0 + πn

Solve

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

Combine all the solutions

x = πn

1 - cos (x) + sin (x) = 0

\frac{12000}{2 \cdot 6380} = tan (\frac{9 0 ^{\circ} - u}{2})

cos^{2} (t) - 3 sin (t) = 3

4 sin^{4} (x) - 4 sin^{2} (x) + 1 = 0

4 sin (θ) + 23 = 0, 0^{\circ} \leq θ \leq 36 0^{\circ}

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