Question 675437
{{{cos(alpha-beta)/cos(alpha)sin(beta) = tan(alpha)+cot(beta)}}}
Since the arguments on the right side are just {{{alpha}}} and {{{beta}}}, I'm going to use the cos(A-B) formula on the numerator of the left side so that all the arguments are {{{alpha}}} or {{{beta}}}:
{{{(cos(alpha)cos(beta) + sin(alpha)sin(beta))/cos(alpha)sin(beta) = tan(alpha)+cot(beta)}}}<br>
Since the right side has two terms I'm going to split the fraction on the left into two terms:
{{{cos(alpha)cos(beta)/cos(alpha)sin(beta) + sin(alpha)sin(beta)/cos(alpha)sin(beta)  = tan(alpha)+cot(beta)}}}<br>
Each of the new fractions will reduce:
{{{cos(beta)/sin(beta) + sin(alpha)/cos(alpha) = tan(alpha)+cot(beta)}}}<br>
The first fraction is cot and the second is tan:
{{{cot(beta) + tan(alpha) = tan(alpha)+cot(beta)}}}<br>
Since addition is commutative we can change the order:
{{{tan(alpha) + cot(beta) = tan(alpha)+cot(beta)}}}