tan(4x-4)=cot(3x+10)

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Solution for tan(4x-4)=cot(3x+10) equation: 


Simplifying
tan(4x + -4) = cot(3x + 10)

Reorder the terms:
ant(-4 + 4x) = cot(3x + 10)
(-4 * ant + 4x * ant) = cot(3x + 10)
(-4ant + 4antx) = cot(3x + 10)

Reorder the terms:
-4ant + 4antx = cot(10 + 3x)
-4ant + 4antx = (10 * cot + 3x * cot)
-4ant + 4antx = (10cot + 3cotx)

Solving
-4ant + 4antx = 10cot + 3cotx

Solving for variable 'a'.

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

Reorder the terms:
-4ant + 4antx + -10cot + -3cotx = 10cot + -10cot + 3cotx + -3cotx

Combine like terms: 10cot + -10cot = 0
-4ant + 4antx + -10cot + -3cotx = 0 + 3cotx + -3cotx
-4ant + 4antx + -10cot + -3cotx = 3cotx + -3cotx

Combine like terms: 3cotx + -3cotx = 0
-4ant + 4antx + -10cot + -3cotx = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-4an + 4anx + -10co + -3cox) = 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 '(-4an + 4anx + -10co + -3cox)' equal to zero and attempt to solve:

Simplifying
-4an + 4anx + -10co + -3cox = 0

Solving
-4an + 4anx + -10co + -3cox = 0

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

Add '10co' to each side of the equation.
-4an + 4anx + -10co + 10co + -3cox = 0 + 10co

Combine like terms: -10co + 10co = 0
-4an + 4anx + 0 + -3cox = 0 + 10co
-4an + 4anx + -3cox = 0 + 10co
Remove the zero:
-4an + 4anx + -3cox = 10co

Add '3cox' to each side of the equation.
-4an + 4anx + -3cox + 3cox = 10co + 3cox

Combine like terms: -3cox + 3cox = 0
-4an + 4anx + 0 = 10co + 3cox
-4an + 4anx = 10co + 3cox

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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