Question 765444

start with right side and prove it's equal to left side:

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

={{{tan(x)/2tan(x)+sin(x)/2tan(x)}}}

={{{(1/2)(tan(x)/tan(x)+sin(x)/tan(x))}}}

={{{(1/2)(1+sin(x)/tan(x))}}}..........since {{{sin(x)/tan(x)=sin(x)/(sin(x)/cos(x))=cross(sin(x))cos(x)/cross((sin(x)))=cos (x)}}}, we have

={{{(1/2)(1+cos(x))}}}

={{{cos^2(x/2)}}}