Докажите тождество: [latex]\frac{1 - cos 2t + sin 2t }{1 + cos 2t + sin 2t} [/latex] * tg ( [latex]\frac{ \pi }{2} [/latex] - t ) = 1

1) 1 - cos2t + sin2t = cos^2t + sin^2t - cos^2t + sin^2t +2sintcost =  = 2sin^2t + 2sintcost = 2sint(sint + cost)   2) 1 + cos2t + sin2t = cos^2t + sin^2t + cos^2t - sin^2t +2sintcost =  = 2cos^2t + 2sintcost = 2cost(cost + sint)   3) tg(П/2 - t) = ctgt   4) 2sint(sint + cost)*ctgt/[2cost(cost + sint)] = tgt*ctgt = 1