Question 976153
There must be a typo, but I cannot guess what it should be.
{{{(1-tan(x))/(1+tan(x))=2cos^2(x)-1}}} is not true for all values of {{{x}}} .
For example, for the angle shown here {{{drawing(200,150,-0.4,4.4,-0.3,3.3,triangle(0,0,4,0,4,3),rectangle(4,0,3.7,0.3),
red(arc(0,0,1.6,1.6,-36.87,0)),locate(0.5,0.4,red(x)),
locate(1.8,0,4),locate(4.1,1.8,3),locate(2,1.5,5) )}}} ,
{{{cos(red(x))=4/5=0.8}}} , {{{sin(red(x))=3/5=0.6)}}} , and {{{tan(red(x))=3/4=0.75}}} .
In that case, 
{{{(1-tan(red(x)))/(1+tan(red(x)))=(1-0.75)/(1+0.75)=0.25/1.75=1/7=about0.143}}} (rounded), and
{{{2cos^2(red(x))-1=2*0.8^2-1=2*0.64-1=1.28-1=0.28}}}