1) докажите тождество: cos(a-90)+sin(a-180)+tg^2(180-a)+ctg^2(a-180)=tg^2(a)+ctg^2(a) 2)sin(t)=5/13 pi> t> pi/2, найти cos(t),tg^2(t),sin^2(t)

Cos(α-90)=cos(-(90-α))=cos(90-α)=sinα
sin(α-180)=sin(-(180-α))=-sin(180-α)=-sinα
tg²(180-α)=(tg(180-α))²=(-tgα)²=tg²α
ctg²(α-180)=(ctg(-(180-α)))²=(-ctg(180-α))²=(ctgα)²=ctg²α

cos(α-90)+sin(α-180)+tg²(180-α)+ctg²(α-180)=sinα-sinα+tg²α+ctg²α=tg²α+ctg²α
tg²α+ctgα=tg²α+ctg²α

2.  sin²t=(5/13)²,  sin²t=25/169 
sin²t+cos²t=1 
cos²t=1-(5/13)², cos²t=144/169
cost=+-12/13, π/2<t<π, ⇒cost<0
cost=-12/13
tg²t=sin²t/cos²t, tg²t=(25/169)/(144/169).
tg²t=25/144