Question 1207649
<pre>
By the way, that notation with backward slashes "\" is not compatible with 
this site, which is written with HTML, so there is no need using it here.

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

Here's an alternate proof, using the fact that any quantity multiplied by
its reciprocal is always 1. 

Start with the left side:

{{{(sin(theta)+tan(theta))/(csc(theta)+cot(theta))}}}

Multiply top and bottom by the "conjugate" of the denominator:

{{{expr((sin(theta)+tan(theta))/(csc(theta)+cot(theta)))}}}{{{""*""}}}{{{expr((csc(theta)-cot(theta))/(csc(theta)-cot(theta)))}}}

{{{(
sin(theta)csc(theta)-sin(theta)cot(theta)+tan(theta)csc(theta)-tan(theta)cot(theta))/(csc^2(theta)-cot^2(theta))}}}

Use the fact that multiplying an expression by its reciprocal is always 1.
Also the denominator is a well-known identity:

{{{(
1-sin(theta)cot(theta)+tan(theta)csc(theta)-1)/1}}}

{{{-sin(theta)cot(theta)+tan(theta)csc(theta)}}}

{{{-sin(theta)expr(cos(theta)/sin(theta))+expr(sin(theta)/cos(theta))expr(1/sin(theta))}}}

{{{-cos(theta)+1/cos(theta)}}}

{{{(-cos^2(theta)+1)/cos(theta)}}}

{{{sin^2(theta)/cos(theta)}}}

{{{(sin(theta)sin(theta))/cos(theta)}}}

{{{sin(theta)*expr(sin(theta)/cos(theta))}}}

{{{sin(theta)*tan(theta)}}}

Edwin</pre>