Question 1119399
<pre>
I have discovered what your copying error in the first
one must have been.  The sign between the terms in the
numerator of the left side should have been +, not -.
{{{tan(x+"45°")+tan(x-"45°")= 4*tan^""(x)/(1-tan^2(x))}}}

Work with left side only:

{{{tan(x+"45°")+tan(x-"45°") }}}
{{{(tan(x)+tan("45°"))/(1-tan(x)*tan("45°"))+(tan(x)-tan("45°"))/(1+tan(x)*tan("45°"))  }}}

{{{(tan(x)+1)/(1-tan(x)*(1))+(tan(x)-1)/(1+tan(x)*(1))  }}}

{{{(tan(x)+1)/(1-tan(x))+(tan(x)-1)/(1+tan(x))  }}}

{{{( (tan(x)^""+1)*(1+tan(x)^"")+(tan(x)^""-1)*(1-tan(x)^"") )/((1-tan(x)^"")*(1+tan(x)^""))  }}}

{{{(( tan^""(x)+tan^2(x)^""+1+tan^""(x)   )+ (tan^""(x)-tan^2(x)^""-1+tan^""(x))) /(1-tan^2(x))}}}

{{{( tan^""(x)+tan^2(x)+1+tan^""(x)   + tan^""(x)-tan^2(x)-1+tan^""(x)) /(1-tan^2(x))}}}

{{{4*tan^""(x)/(1-tan^2(x))}}}

----------------------------------------------------------

{{{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 (aka AnlytcPhil) </pre>