tan(3x+30)=cot(x-4)

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Solution for tan(3x+30)=cot(x-4) equation: 


Simplifying
tan(3x + 30) = cot(x + -4)

Reorder the terms:
ant(30 + 3x) = cot(x + -4)
(30 * ant + 3x * ant) = cot(x + -4)
(30ant + 3antx) = cot(x + -4)

Reorder the terms:
30ant + 3antx = cot(-4 + x)
30ant + 3antx = (-4 * cot + x * cot)
30ant + 3antx = (-4cot + cotx)

Solving
30ant + 3antx = -4cot + cotx

Solving for variable 'a'.

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

Reorder the terms:
30ant + 3antx + 4cot + -1cotx = -4cot + 4cot + cotx + -1cotx

Combine like terms: -4cot + 4cot = 0
30ant + 3antx + 4cot + -1cotx = 0 + cotx + -1cotx
30ant + 3antx + 4cot + -1cotx = cotx + -1cotx

Combine like terms: cotx + -1cotx = 0
30ant + 3antx + 4cot + -1cotx = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(30an + 3anx + 4co + -1cox) = 0


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

Simplifying
t = 0

Solving
t = 0

Move all terms containing a 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 + 4co + -1cox)' equal to zero and attempt to solve:

Simplifying
30an + 3anx + 4co + -1cox = 0

Solving
30an + 3anx + 4co + -1cox = 0

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

Add '-4co' to each side of the equation.
30an + 3anx + 4co + -4co + -1cox = 0 + -4co

Combine like terms: 4co + -4co = 0
30an + 3anx + 0 + -1cox = 0 + -4co
30an + 3anx + -1cox = 0 + -4co
Remove the zero:
30an + 3anx + -1cox = -4co

Add 'cox' to each side of the equation.
30an + 3anx + -1cox + cox = -4co + cox

Combine like terms: -1cox + cox = 0
30an + 3anx + 0 = -4co + cox
30an + 3anx = -4co + cox

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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