1)ctga=-3
sin²a=1: (1+ctg²a)=1:(1+9)=1/10
sina=-1/√10
cosa=√1-1/10=3/√10
tga=-1/3
2)1/cos²a-tg²a-sin²a=1+tg²a-tg²a-sin²a=1-sin²a=cos²a
(tg²a-sin²a)(1/sin²a -1)=(tg²a-sin²a)*ctg²a=tg²a-sin²a*ctg²a=1-cos²a=sin²a
tg(π+a)sin(π/2-a)/cos(3π/2+a)=tga*cosa/sina=tga*ctga=1
3)(cos²a-sin²a)*(cos²a+sin²a)/(1-sina)(1+sina) +2tg²a=cos2a/cos²a +2sin²a/cos²a=
=(cos²a-sin²a+2sin²a)/cos²a=(sin²a+cos²a)/cos²a=1/cos²a
1/cos²a=1/cos²a
4)ctg(-420)=ctg(-60)=-ctg60=-1/√3
sin(-21π/4)=-sin(π+π/4)=√2/2
cos10π/3+sin150=cos(π+π/3) +sin(180-30)=-cosπ/3+sin30=-1/2+1/2=0