tan(3x+4)=cot(5x-10)

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Solution for tan(3x+4)=cot(5x-10) equation: 


Simplifying
tan(3x + 4) = cot(5x + -10)

Reorder the terms:
ant(4 + 3x) = cot(5x + -10)
(4 * ant + 3x * ant) = cot(5x + -10)
(4ant + 3antx) = cot(5x + -10)

Reorder the terms:
4ant + 3antx = cot(-10 + 5x)
4ant + 3antx = (-10 * cot + 5x * cot)
4ant + 3antx = (-10cot + 5cotx)

Solving
4ant + 3antx = -10cot + 5cotx

Solving for variable 'a'.

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

Reorder the terms:
4ant + 3antx + 10cot + -5cotx = -10cot + 10cot + 5cotx + -5cotx

Combine like terms: -10cot + 10cot = 0
4ant + 3antx + 10cot + -5cotx = 0 + 5cotx + -5cotx
4ant + 3antx + 10cot + -5cotx = 5cotx + -5cotx

Combine like terms: 5cotx + -5cotx = 0
4ant + 3antx + 10cot + -5cotx = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(4an + 3anx + 10co + -5cox) = 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 + 3anx + 10co + -5cox)' equal to zero and attempt to solve:

Simplifying
4an + 3anx + 10co + -5cox = 0

Solving
4an + 3anx + 10co + -5cox = 0

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

Add '-10co' to each side of the equation.
4an + 3anx + 10co + -10co + -5cox = 0 + -10co

Combine like terms: 10co + -10co = 0
4an + 3anx + 0 + -5cox = 0 + -10co
4an + 3anx + -5cox = 0 + -10co
Remove the zero:
4an + 3anx + -5cox = -10co

Add '5cox' to each side of the equation.
4an + 3anx + -5cox + 5cox = -10co + 5cox

Combine like terms: -5cox + 5cox = 0
4an + 3anx + 0 = -10co + 5cox
4an + 3anx = -10co + 5cox

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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