Question 608410
Can you prove this identity:

{{{sin(3x)/sin(x)}}} - {{{cos(3x)/cos(x)}}} = 2
<pre>
Get an LCD on the left side of sin(x)·cos(x) 

{{{(sin(3x)cos(x)-cos(3x)sin(x))/(sin(x)cos(x))}}}

Use the identity sin(A)cos(B)-cos(A)sin(B) = sin(A-B) 

{{{sin(3x-x)/(sin(x)cos(x))}}}

{{{sin(2x)/(sin(x)cos(x))}}}

Use the identity sin(2&#952;) = 2sin(&#952;)·cos(&#952;)

{{{(2sin(x)cos(x))/(sin(x)cos(x))}}}

{{{(2cross(sin(x))cross(cos(x)))/(cross(sin(x))cross(cos(x)))}}}

2

Edwin</pre>