ptanx+qtany=tanz

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Solution for ptanx+qtany=tanz equation: 


Simplifying
ptanx + qtany = tanz

Solving
anptx + anqty = antz

Solving for variable 'a'.

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

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

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

Factor out the Greatest Common Factor (GCF), 'ant'.
ant(px + qy + -1z) = 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 + -1z)' equal to zero and attempt to solve:

Simplifying
px + qy + -1z = 0

Solving
px + qy + -1z = 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 + -1z = 0 + -1px

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

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

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

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

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

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

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

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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