cot = 1/tan so this becomes:
1/tan -abtan=a-b
tan is the common denominator on the left. Add the factors on the left over tan, the common denominator.
1 is already over the common denominator so it stays the same. abtan is over 1, so to put it over tan, multiply tan * (abtan) = ab(tan)^2
(1-ab(tan)^2)/tan = a-b
1-ab(tan)^2 = (a-b)tan
1-ab(tan)^2 - (a-b)tan = 0
Multiply everything by -1. and call tan=x to make it easier to manipulate.
abx^2 + (a-b)x - 1 = 0.
Reverse foil.
(ax - 1)(bx + 1)=0
ax-1=0 thus ax=1 and x=1/a.
bx+1=0 thus bx=-1 and x=-1/b
Remember that x=tan so this is tan = 1/a or -1/b
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