Question

Помогите пожалуйста,срочно!!!Упростить:
1) (tgt+ctgt)2 – (tgt – ctgt)2; 2) sin2tcos2t(tg2t+ctg2t +2)

Answer 1

(tgt+ctgt)²-(tgt-ctgt)²=tg²t+2tgt*ctgt+ctg²-(tg²t-2tgt*ctgt+ctg²t)=2tgt*ctgt=4*1=4

sin2tcos2t*(tgt+ctgt+2)=1+sin4t

1. tg2t+ctg2t=sin2t/cos2t+cos2t/sin2t=(sin²2t+cos²2t)/(sin2t*cos2t)=1/(sin2t*cos2t)
2. sin2t*cos2t*(1/sin2t*cos2t+2)=sin2t*cos2t*(1+2sin2t*cos2t)/(sin2t*cos2t)=1+sin4t