Question 1157401
<pre>
{{{5tan(3x) = (15tan(x) - 5tan^3(x))/ (1 - 3tan^2(x))}}}

We will work only with the left side.  We will use this formulas:

               {{{tan^""(A+B)=(tan^""(A)+tan^""(B))/(1-tan^""(A)tan^""(B))}}} 

               and its corollary:

               {{{tan^""(2theta)=(2tan^""(theta))/(1-tan^2(theta))}}} 


{{{matrix(7,2,

5tan(3x),""="",
"","",
5tan(2x+x),""="",
"","",
5(tan(2x)+tan(x))/(1-tan(2x)tan(x)),""="",
"","",
5(expr((2tan^""(x))/(1-tan^2(x)))+tan(x))/(1-expr((2tan^""(x))/(1-tan^2(x)))tan(x)),""=""

)}}}

Distribute the 5 to remove parentheses on the top and
multiply tangents on the bottom:

{{{matrix(1,2,
expr((10tan^""(x))/(1-tan^2(x))+5tan(x))/(1-expr((2tan^2(x))/(1-tan^2(x)))),""="" )}}}

{{{matrix(1,2,
( 10tan^""(x)+5tan^""(x)(1-tan^2(x)^"") )/( 1*(1-tan^2(x)^"")-2tan^2(x)),""="")}}}

Distribute to remove the parentheses:

{{{matrix(1,2,
( 10tan^""(x)+5tan^""(x)-5tan^2(x) )/(1-tan^2(x)-2tan^2(x)),""="")}}}

Combine terms:

{{{(15tan(x) - 5tan^3(x))/ (1 - 3tan^2(x))}}}

Edwin</pre>