tan(3x+5)=cot(2x+10)

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Solution for tan(3x+5)=cot(2x+10) equation: 


Simplifying
tan(3x + 5) = cot(2x + 10)

Reorder the terms:
ant(5 + 3x) = cot(2x + 10)
(5 * ant + 3x * ant) = cot(2x + 10)
(5ant + 3antx) = cot(2x + 10)

Reorder the terms:
5ant + 3antx = cot(10 + 2x)
5ant + 3antx = (10 * cot + 2x * cot)
5ant + 3antx = (10cot + 2cotx)

Solving
5ant + 3antx = 10cot + 2cotx

Solving for variable 'a'.

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

Reorder the terms:
5ant + 3antx + -10cot + -2cotx = 10cot + -10cot + 2cotx + -2cotx

Combine like terms: 10cot + -10cot = 0
5ant + 3antx + -10cot + -2cotx = 0 + 2cotx + -2cotx
5ant + 3antx + -10cot + -2cotx = 2cotx + -2cotx

Combine like terms: 2cotx + -2cotx = 0
5ant + 3antx + -10cot + -2cotx = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(5an + 3anx + -10co + -2cox) = 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 '(5an + 3anx + -10co + -2cox)' equal to zero and attempt to solve:

Simplifying
5an + 3anx + -10co + -2cox = 0

Solving
5an + 3anx + -10co + -2cox = 0

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

Add '10co' to each side of the equation.
5an + 3anx + -10co + 10co + -2cox = 0 + 10co

Combine like terms: -10co + 10co = 0
5an + 3anx + 0 + -2cox = 0 + 10co
5an + 3anx + -2cox = 0 + 10co
Remove the zero:
5an + 3anx + -2cox = 10co

Add '2cox' to each side of the equation.
5an + 3anx + -2cox + 2cox = 10co + 2cox

Combine like terms: -2cox + 2cox = 0
5an + 3anx + 0 = 10co + 2cox
5an + 3anx = 10co + 2cox

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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