Question 279019
{{{sin(x)tan(x/2)=1-cos(x)}}}
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There are two half-angle identities for {{{tan(theta/2)}}}

They are 

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

and

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

We will use the second one:

{{{sin(x)tan(x/2)=1-cos(x)}}}

{{{sin(x)((1-cos(x))/sin(x))=1-cos(x)}}}

{{{cross(sin(x))((1-cos(x))/cross(sin(x)))=1-cos(x)}}}

{{{1-cos(x)=1-cos(x)}}}

Edwin</pre>