Question 1042004
<pre>
{{{(cos("60°"-A)+sin("30°"-A))/(cos("30°"-A)-sin("60°"-A))}}}{{{""=""}}}{{{cot(A)}}}

Work with the left side:

Use cos(<font face="symbol">a</font>-<font face="symbol">b</font>) = cos(<font face="symbol">a</font>)cos(<font face="symbol">b</font>) + sin(<font face="symbol">a</font>)sin(<font face="symbol">b</font>)
and sin(<font face="symbol">a</font>-<font face="symbol">b</font>) = sin(<font face="symbol">a</font>)cos(<font face="symbol">b</font>) - cos(<font face="symbol">a</font>)sin(<font face="symbol">b</font>)

{{{((cos("60°")cos(A)^"" + sin("60°")sin(A))+(sin("30°")cos(A)^"" - cos("30°")sin(A)))/((cos("30°")cos(A)^"" + sin("30°")sin(A))-(sin("60°")cos(A)^"" - cos("60°")sin(A)))}}}

Remove parentheses.  Be careful to make sign change on 
last term of denominator.

{{{(cos("60°")cos(A) + sin("60°")sin(A)+sin("30°")cos(A) - cos("30°")sin(A))/(cos("30°")cos(A) + sin("30°")sin(A)-sin("60°")cos(A) + cos("60°")sin(A))}}}

Use the fact that {{{cos("60°")=sin("30°")=1/2}}} and {{{sin("60°")=cos("30°")=sqrt(3)/2}}}

{{{(expr(1/2)cos(A) + expr(sqrt(3)/2)sin(A)+expr(1/2)cos(A) - expr(sqrt(3)/2)sin(A))/(expr(sqrt(3)/2)cos(A) + expr(1/2)sin(A)-expr(sqrt(3)/2)cos(A) + expr(1/2)sin(A))}}}


{{{(expr(1/2)cos(A) + cross(expr(sqrt(3)/2)sin(A))+expr(1/2)cos(A) - cross(expr(sqrt(3)/2)sin(A)))/(cross(expr(sqrt(3)/2)cos(A)) + expr(1/2)sin(A)-cross(expr(sqrt(3)/2)cos(A)) + expr(1/2)sin(A))}}}

{{{(expr(1/2)cos(A) +expr(1/2)cos(A))/(expr(1/2)sin(A) + expr(1/2)sin(A))}}}

{{{cos(A)/sin(A)}}}

  Use {{{cot(theta)=cos(theta)/sin(theta)}}}

{{{cot(A)}}}

Edwin</pre>