Question 838594
We will use the equivalent expressions sin(2x) = 2 sin x cos x 
Since sin(a) = 1/2 and sin(a) = (opposite side)/hypotenuse
To find the relative length of the third leg
{{{1^2 + t^2 = 2^2}}}
{{{1 + t^2 = 4}}}
{{{t^2 = 3}}}
{{{t = sqrt(3)}}}
opp = 1 , adj = sqrt(3) , hyp =  2
Since cos(x) = adj/hyp ,
cos(a) = sqrt(3)/2
Substituting sqrt(3)/2 for cos(a) and 1/2 for sin(a) in 2sin(a)*cos(a)
2*(1/2)(sqrt(3)/2) = (sqrt(3)/2)
Now we have 
sin(2a)= {{{(sqrt(3)/2)}}}
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cos(2a) = cos^2(a) - sin^2(a)
cos(2a) = {{{(sqrt(3)/2)^2 - (1/2)^2}}}
cos(2a) = {{{3/4 - 1/4}}}
cos(2a) = {{{2/4}}}
cos(2a) = {{{1/2}}}
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tan(2a) = sin(2a)/cos(2a) 
= {{{(sqrt(3)/2) / ( 1/2 )}}}
= {{{sqrt(3)}}}
Summarizing
sin(2a)= {{{(sqrt(3)/2)}}},cos(2a) = {{{1/2}}},tan(2a) = {{{sqrt(3)}}}
You may have noticed that for sin(a) = 1/2 a is 30 degrees
sin(60)= {{{(sqrt(3)/2)}}},cos(60) = {{{1/2}}},tan(60) = {{{sqrt(3)}}}