tan(2x)=tan(x+30)

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Solution for tan(2x)=tan(x+30) equation: 


Simplifying
tan(2x) = tan(x + 30)

Remove parenthesis around (2x)
ant * 2x = tan(x + 30)

Reorder the terms for easier multiplication:
2ant * x = tan(x + 30)

Multiply ant * x
2antx = tan(x + 30)

Reorder the terms:
2antx = ant(30 + x)
2antx = (30 * ant + x * ant)
2antx = (30ant + antx)

Solving
2antx = 30ant + antx

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-30ant' to each side of the equation.
-30ant + 2antx = 30ant + -30ant + antx

Combine like terms: 30ant + -30ant = 0
-30ant + 2antx = 0 + antx
-30ant + 2antx = antx

Add '-1antx' to each side of the equation.
-30ant + 2antx + -1antx = antx + -1antx

Combine like terms: 2antx + -1antx = 1antx
-30ant + 1antx = antx + -1antx

Combine like terms: antx + -1antx = 0
-30ant + 1antx = 0

Factor out the Greatest Common Factor (GCF), 'ant'.
ant(-30 + x) = 0


Subproblem 1
Set the factor 'ant' equal to zero and attempt to solve:

Simplifying
ant = 0

Solving
ant = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying
ant = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-30 + x)' equal to zero and attempt to solve:

Simplifying
-30 + x = 0

Solving
-30 + x = 0

Move all terms containing a to the left, all other terms to the right.

Add '30' to each side of the equation.
-30 + 30 + x = 0 + 30

Combine like terms: -30 + 30 = 0
0 + x = 0 + 30
x = 0 + 30

Combine like terms: 0 + 30 = 30
x = 30

Add '-1x' to each side of the equation.
x + -1x = 30 + -1x

Combine like terms: x + -1x = 0
0 = 30 + -1x

Simplifying
0 = 30 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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