A)(3sint+4cost)² +(4sint-3cost)²=
=9sin²t+24sintcost+16cos²t+16sin²t-24sintcost+9cos²t=
=25sin²t+25cos²t=25(sin²t+cos²t)=25;
б) (tgt+ctgt)² -(tgt-ctgt)²=tg²t+2tgt·ctgt+ctg²t-tg²t+2tgt·ctgt-ctg²t=
=4tgt·ctgt=4;
в)sint·cost(tgt+ctgt)=sint·cost·tgt+sint·cost·ctgt=sin²t·cost/cost+cos²t·sint/sint=
sin²t+cos²t=1;
г) sin²t·cos²t(tg²t+ctg²t+2)=sin⁴t·cos²t/cos²t+cos⁴t·sin²t/sin²t+2sin²t·cos²t=
=sin⁴t+cos⁴t+2sin²tcos²t=(sin²t+cos²t)²=1²=1;