Question 1067577

From the figure, find the exact values of sin 2u, cos 2u, and tan 2u
Figure: https://s30.postimg.org/5bufl6abl/figure_23.png
Thank you!
<pre>Opposite side: 2           Adjacent side: 1          {{{r^2 = 2^2 + 1^2}}}
                                                     {{{r^2 = 4 + 1}}}
                                                     Hypotenuse, or r = {{{sqrt(5)}}}

{{{sin (u) = 2sqrt(5)/5}}}               {{{cos (u) = sqrt(5)/5}}}               {{{tan (u) = 2}}}

{{{sin (2u)}}}  = {{{2 sin (u) cos (u)}}}
{{{highlight_green(sin (2u))}}} = {{{highlight_green(matrix(1,9, 2(2sqrt(5)/5) * (sqrt(5)/5), "=", (4sqrt(5)/5) * (sqrt(5)/5), "=", 4(5)/25, "=", 4(cross(5))/5cross(25), "=", highlight(4/5)))}}}



{{{cos (2u)}}}  = {{{2 cos^2 (u) - 1}}}
{{{highlight_green(cos (2u))}}} = {{{highlight_green(matrix(1,11, 2(sqrt(5)/5)^2 - 1, "=", 2(5/25) - 1, "=", 10/25 - 1, "=", 10/25 - 25/25, "=", - 15/25, "=", highlight(- 3/5)))}}}



{{{tan (2u)}}}  = {{{(2 tan (u))/(1 - tan^2 (u))}}}
{{{highlight_green(tan (2u))}}} = {{{highlight_green(matrix(1,5, 2(2)/(1 - 2^2), "=", 4/(1 - 4), "=", highlight(matrix(1,3, 4/- 3, or, - 4/3))))}}}</pre>