Question 843054
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Hi,
sin(x + y) = sin x cosy  +  cos x sin y
sin(x - y) = sin x cosy  -  cos x sin y
{{{sin(x+y)/sin(x-y) =(sin(x)cos(y)  +  cos(x)sin(y))/(sin(x)cos(y)  -  cos(x)sin(y)) = (tan(x)cot(y) + 1)/(tan(x)cot(y) - 1) = 2/3}}} Dividing Numerator and Denominator by cos(x)sin(y)
{{{(tan(x)cot(y) + 1)/(tan(x)cot(y) - 1) = 2/3}}}   Cross Multiplying to solve for tan(x)cot(y)