Question 746612
<pre>
{{{(csc(x)+sec(x))/(sin(x)+cos(x))}}}{{{""=""}}}{{{cos(x)+tan(x)}}}

Sorry, but that is not an identity.

I will show that it does not hold in the case of the 3-4-5 right
triangle, where x is the smaller acute angle:

{{{drawing(200,160,-.5,4.5,-.5,3.5, triangle(0,0,4,0,4,3),
locate(2,0,4),locate(4.1,1.5,3),locate(2,2,5),locate(.8,.5,x),
red(arc(0,0,3,-3,0,37))

 )}}}{{{matrix(2,5,

sin(x)=3/5, "",cos(x)=4/5,"", tan(x)=3/4,
csc(x)=5/3, "", sec(x)=5/4, "", cot(x)=4/3)}}}

{{{(csc(x)+sec(x))/(sin(x)+cos(x))}}}{{{""=""}}}{{{cos(x)+tan(x)}}}

{{{(5/3+5/4)/(3/5+4/5)}}}{{{""=""}}}{{{4/5+3/4}}}

{{{(20/12+15/12)/(7/5)}}}{{{""=""}}}{{{16/20+15/20}}}

{{{(35/12)/(7/5)}}}{{{""=""}}}{{{31/20}}}

{{{(35/12)*(5/7)}}}{{{""=""}}}{{{31/20}}}

{{{(cross(35)^5/12)*(5/cross(7))}}}{{{""=""}}}{{{31/20}}}

{{{25/12}}}{{{""=""}}}{{{31/20}}}

That is false, so the equation is not an identity

Edwin</pre>