Доказать тождество (рисунок внутри) (sin t + cos t)² -1 = 2ctg² t tgt - sin t cos t

((sint+cost)²-1)/(tgt-sintcost)=((sin²t+2sintcost+cos²t)-1)/(sint/cost-sintcost)=2sintcost/(sint(1/cost-cost))=2cost/((1-cos²t)/cost)=2cos²t/(1-cos²t)=2cos²t/sin²t=2ctg²t