Question 1189035
<pre>

{{{cos(x) = (2sqrt(5))/5 = adjacent/hypotenuse}}}

Draw a right triangle with angle x, adjacent side=2√5 and hypotenuse=5, then
use Pythagorean theorem to get the opposite side. Then simplify the opposite
side.

{{{drawing(400,800/3,-.3,2.7,-.5,1.5,
locate(1.65,.9,90^o-x),
triangle(0,0,2,0,2,1),
locate(1,-.05,2sqrt(5)),
locate(.9,.6,5),locate(.3,.15,x),
locate(2,.6,sqrt(5^2-(2sqrt(5))^2)) )}}}

{{{drawing(400,800/3,-.3,2.7,-.5,1.5,
locate(1.65,.9,90^o-x),
triangle(0,0,2,0,2,1),
locate(1,-.05,2sqrt(5)),
locate(.9,.6,5),locate(.3,.15,x),
locate(2,.6,sqrt(25-(4*5))) )}}}

{{{drawing(400,800/3,-.3,2.7,-.5,1.5,
locate(1.65,.9,90^o-x),
triangle(0,0,2,0,2,1),
locate(1,-.05,2sqrt(5)),
locate(.9,.6,5),locate(.3,.15,x),
locate(2,.6,sqrt(25-20))) )}}}

{{{drawing(400,800/3,-.3,2.7,-.5,1.5,
locate(1.65,.9,90^o-x),
triangle(0,0,2,0,2,1),
locate(1,-.05,2sqrt(5)),
locate(.9,.6,5),locate(.3,.15,x),
locate(2.04,.6,sqrt(5))) )}}}

{{{tan(90^o-x)}}}{{{""=""}}}{{{opposite/adjacent}}}{{{""=""}}}{{{(2sqrt(5))/sqrt(5)}}}{{{""=""}}}{{{2}}}

Edwin</pre>