Question 1107091
<pre>
There is no online calculator that will solve identities
like this:

{{{2csc(x)=tan(expr(1/2)x)+cot(expr(1/2)x)}}}

Let's get the right tools:

There are two formulas for {{{tan(expr(1/2)theta)}}}

which don't involve square roots.  They are:

{{{tan(expr(1/2)theta)}}}{{{""=""}}}{{{(1-cos(theta))/sin(theta)}}}

and

{{{tan(expr(1/2)theta)}}}{{{""=""}}}{{{sin(theta)/(1+cos(theta))}}}

and since the cotangent is the reciprocal of the tangent, we can
make two formulas from them for {{{cot(expr(1/2)theta)}}}

{{{cot(expr(1/2)theta)}}}{{{""=""}}}{{{sin(theta)/(1-cos(theta))}}}

and  

{{{cot(expr(1/2)theta)}}}{{{""=""}}}{{{(1+cos(theta))/sin(theta)}}}

Let's pick two of them for the right side of the identity which
have the same denominator so they'll be easy to add.  Pick the 
ones with sin(x) denominators to substitute in the right side 
of the identity, which is:

{{{tan(expr(1/2)x)+cot(expr(1/2)x)}}}

Substituting:

{{{(1-cos(x))/sin(x)}}}{{{""+""}}}{{{(1+cos(x))/sin(x)}}}

{{{((1-cos(x)^"")+(1+cos(x)^""))/sin(x)^""}}}

{{{(1-cos(x)^""+1+cos(x)^"")/sin(x)^""}}}

{{{(1-cross(cos(x)^"")+1+cross(cos(x)^""))/sin(x)^""}}}

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

{{{2*(1/sin(x))}}}

{{{2csc(x)}}}

Edwin</pre>