Question

Докажите тождество: sin2t/1+cos2t*cost/1+cost=tgt/2 sin2t/1+cos2t*cost/1+cost*cos1/2/1+cost t/2=tg1/4

Answer 1

1)tgt/2=sint/(1+cost)
sin2t/(1+cos2t) *cost/(1+cost)=2sintcost*cost/2cos²t(1+cost)=sint/(1+cost)=tgt/2
2)sin2t/(1+cos2t)*cost/(1+cost)*cost/2/(1+cost t/2)=tgt/2*cost/2/(1+cost t/2)=
=sint/2*cost/2/cost/2*(1+cost/2)=sint/2/(1+cost/2)=tgt/4