Cot(x+20)=tan(3x+30)

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Solution for Cot(x+20)=tan(3x+30) equation: 


Simplifying
Cot(x + 20) = tan(3x + 30)

Reorder the terms:
otC(20 + x) = tan(3x + 30)
(20 * otC + x * otC) = tan(3x + 30)
(20otC + otxC) = tan(3x + 30)

Reorder the terms:
20otC + otxC = ant(30 + 3x)
20otC + otxC = (30 * ant + 3x * ant)
20otC + otxC = (30ant + 3antx)

Solving
20otC + otxC = 30ant + 3antx

Solving for variable 'o'.

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

Reorder the terms:
-30ant + -3antx + 20otC + otxC = 30ant + 3antx + -30ant + -3antx

Reorder the terms:
-30ant + -3antx + 20otC + otxC = 30ant + -30ant + 3antx + -3antx

Combine like terms: 30ant + -30ant = 0
-30ant + -3antx + 20otC + otxC = 0 + 3antx + -3antx
-30ant + -3antx + 20otC + otxC = 3antx + -3antx

Combine like terms: 3antx + -3antx = 0
-30ant + -3antx + 20otC + otxC = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-30an + -3anx + 20oC + oxC) = 0


Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Add '-1t' to each side of the equation.
t + -1t = 0 + -1t
Remove the zero:
0 = -1t

Simplifying
0 = -1t

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 '(-30an + -3anx + 20oC + oxC)' equal to zero and attempt to solve:

Simplifying
-30an + -3anx + 20oC + oxC = 0

Solving
-30an + -3anx + 20oC + oxC = 0

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

Add '30an' to each side of the equation.
-30an + -3anx + 20oC + 30an + oxC = 0 + 30an

Reorder the terms:
-30an + 30an + -3anx + 20oC + oxC = 0 + 30an

Combine like terms: -30an + 30an = 0
0 + -3anx + 20oC + oxC = 0 + 30an
-3anx + 20oC + oxC = 0 + 30an
Remove the zero:
-3anx + 20oC + oxC = 30an

Add '3anx' to each side of the equation.
-3anx + 20oC + 3anx + oxC = 30an + 3anx

Reorder the terms:
-3anx + 3anx + 20oC + oxC = 30an + 3anx

Combine like terms: -3anx + 3anx = 0
0 + 20oC + oxC = 30an + 3anx
20oC + oxC = 30an + 3anx

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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