ptanx+qtany=tanzv

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Solution for ptanx+qtany=tanzv equation: 


Simplifying
ptanx + qtany = tanzv

Solving
anptx + anqty = antvz

Solving for variable 'a'.

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

Add '-1antvz' to each side of the equation.
anptx + anqty + -1antvz = antvz + -1antvz

Combine like terms: antvz + -1antvz = 0
anptx + anqty + -1antvz = 0

Factor out the Greatest Common Factor (GCF), 'ant'.
ant(px + qy + -1vz) = 0


Subproblem 1
Set the factor 'ant' equal to zero and attempt to solve:

Simplifying
ant = 0

Solving
ant = 0

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

Simplifying
ant = 0

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 '(px + qy + -1vz)' equal to zero and attempt to solve:

Simplifying
px + qy + -1vz = 0

Solving
px + qy + -1vz = 0

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

Add '-1px' to each side of the equation.
px + qy + -1px + -1vz = 0 + -1px

Reorder the terms:
px + -1px + qy + -1vz = 0 + -1px

Combine like terms: px + -1px = 0
0 + qy + -1vz = 0 + -1px
qy + -1vz = 0 + -1px
Remove the zero:
qy + -1vz = -1px

Add '-1qy' to each side of the equation.
qy + -1qy + -1vz = -1px + -1qy

Combine like terms: qy + -1qy = 0
0 + -1vz = -1px + -1qy
-1vz = -1px + -1qy

Add 'vz' to each side of the equation.
-1vz + vz = -1px + -1qy + vz

Combine like terms: -1vz + vz = 0
0 = -1px + -1qy + vz

Simplifying
0 = -1px + -1qy + vz

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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