Question 675439
{{{(tan(alpha+beta)-tan(beta))/(1+tan(alpha+beta)tan(beta)) =tan(alpha)}}}<br>
{{{tan(A-B) = (tan(A) - tan(B))/(1+tan(A)tan(B))}}}
The left side of your equation matches the pattern of the right side of tan(A-B) with the "A" being {{{alpha+beta}}} and the "B" being {{{beta}}}. So it can be rewritten as a tan(A-B):
{{{tan((alpha+beta)-(beta)) = tan(alpha)}}}
which simplifies to:
{{{tan(alpha) = tan(alpha)}}}
And we're done!