Question 1119399
<pre>
{{{

tan(x+"45°")-tan(x-"45°")= 4*tan(x)/(1-tan^2(x))}}}

That's not true, for if you substitute x = 100°,
you get 45.71229319 = -3.585054968, so
you must have copied it wrong.

But the second one is true:

{{{sin(x-"30°")-cos(x+"60°")=sqrt(3)*sin(x)-cos(x) }}}

Work with left side only:

{{{sin(x-"30°")-cos(x+"60°") }}}
{{{(sin(x)*cos("30°")^""-cos(x)*sin("30°")^"")-(cos(x)*cos("60°")^""-sin(x)*sin("60°")^"")  }}}
{{{(sin(x)*expr(sqrt(3)/2)^""-cos(x)*expr(1/2)^"")-(cos(x)*expr(1/2)^""-sin(x)*expr(sqrt(3)/2)^"")  }}}
{{{(expr(sqrt(3)/2)*sin(x)^""-expr(1/2)*cos(x)^"")-(expr(1/2)*cos(x)^""-expr(sqrt(3)/2)*sin(x)^"")  }}}
{{{expr(sqrt(3)/2)*sin(x)^""-expr(1/2)*cos(x)^""-expr(1/2)*cos(x)^""+expr(sqrt(3)/2)*sin(x)^""  }}}
 {{{expr(sqrt(3)/2)*sin(x)^""+expr(sqrt(3)/2)*sin(x)^""-expr(1/2)*cos(x)^""-expr(1/2)*cos(x)^""  }}}
{{{sqrt(3)*sin(x)-cos(x)}}}

Edwin</pre>