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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