Question 1048627
{{{int((cos2x-1)/(cos2x+1), dx, 0,pi/4)}}}.


{{{(cos2x-1)/(cos2x+1) = (cos^2(x) - sin^2(x)- sin^2(x) - cos^2(x))/(cos^2(x) - sin^2(x)+ sin^2(x)+cos^2(x)) = (-2sin^2(x))/(2cos^2(x)) = -tan^2(x) = 1-sec^2(x)}}}


===> {{{int((cos2x-1)/(cos2x+1), dx, 0,pi/4) = int((1-sec^2(x)), dx, 0,pi/4)}}}

= {{{(x - tanx)[0]^(pi/4) = pi/4 - tan(pi/4) - 0 + tan0 = highlight(pi/4 - 1)}}}.