(1 + cos2t - sin2t)/(1 + sin2t + cos2t) = (cos^2(t) + sin^2(t) + cos^2(t) - sin^2(t) - 2sintcost)/(cos^2(t) + sin^2(t) + 2sintcost + cos^2(t) - sin^2(t)) = (2cos^2(t) - 2sintcost)/(2cos^2(t) + 2sintcost) = (cos^2(t) - sintcost)/(cos^2(t) + sintcost) = (cost - sint)/(cost + sint)
по формуле
bcosx + asinx = sqrt(a^2 + b^2)sin(x + w)
sinw = b/sqrt(a^2 + b^2); cosw = a/sqrt(a^2 + b^2)
(cost - sint)/(cost + sint) = (sqrt(2)sin(t + 3П/4))/(sqrt(2)sin(t + П/4) = sin(t + 3П/4)/sin(t + П/4) = sin(П - (П/4 - t))/sin(П/2 - (П/4 - t)) = sin(П/4 - t)/cos(П/4 - t) = tg(П/4 - t)
чтд