4)
(1-sin²t)(1+tg²t)=1
cos²t * (1+sin²t /cos²t)=1
cos²t * (cos²t+sin²t)/cos²t=1
cos²t+sin²t=1
1≡1 (доказано)
2)
2*tgt *(1-sin²t) = 2*sint/cost *cos²t= 2*sint*cost =sin(2t)
7cos²t - 5 + 7sin²t =7(cos²t+sin²t) - 5 = 7-5=2
sin(-t) +cos(-t) *tg(-t) =sin(-t) +cos(-t) * sin(-t)/cos(-t) =
=sin(-t)+sin(-t) =2sin(-t) = -2sint
5)
формулы: sin(π-t) =sin(t); sin(π/2-t) = cost; tg(π-t) =-tgt .
(sin²(π-t) + sin²(π/2 -t) )* tg(π-t) /sin(π-t) =
= ( - (sin²t+cos²t)*sint/cost ) /sint = -1/cost = - sect (секанс t)