tan(x+15)=cot(2x-30)

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Solution for tan(x+15)=cot(2x-30) equation: 


Simplifying
tan(x + 15) = cot(2x + -30)

Reorder the terms:
ant(15 + x) = cot(2x + -30)
(15 * ant + x * ant) = cot(2x + -30)
(15ant + antx) = cot(2x + -30)

Reorder the terms:
15ant + antx = cot(-30 + 2x)
15ant + antx = (-30 * cot + 2x * cot)
15ant + antx = (-30cot + 2cotx)

Solving
15ant + antx = -30cot + 2cotx

Solving for variable 'a'.

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

Reorder the terms:
15ant + antx + 30cot + -2cotx = -30cot + 30cot + 2cotx + -2cotx

Combine like terms: -30cot + 30cot = 0
15ant + antx + 30cot + -2cotx = 0 + 2cotx + -2cotx
15ant + antx + 30cot + -2cotx = 2cotx + -2cotx

Combine like terms: 2cotx + -2cotx = 0
15ant + antx + 30cot + -2cotx = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(15an + anx + 30co + -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 '(15an + anx + 30co + -2cox)' equal to zero and attempt to solve:

Simplifying
15an + anx + 30co + -2cox = 0

Solving
15an + anx + 30co + -2cox = 0

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

Add '-30co' to each side of the equation.
15an + anx + 30co + -30co + -2cox = 0 + -30co

Combine like terms: 30co + -30co = 0
15an + anx + 0 + -2cox = 0 + -30co
15an + anx + -2cox = 0 + -30co
Remove the zero:
15an + anx + -2cox = -30co

Add '2cox' to each side of the equation.
15an + anx + -2cox + 2cox = -30co + 2cox

Combine like terms: -2cox + 2cox = 0
15an + anx + 0 = -30co + 2cox
15an + anx = -30co + 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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