Răspuns:
Explicație pas cu pas:
AB=12√2cm AC=6√!0
BC²=AB²+AC²=288+360=648
a)sin C=AB/BC=6√10/648=√10/108
cosC=AC/BC=12√2/648=√2/54
tg C=sinC/cosC=√10/108×54/√2=√5/2
ctg C=2√5/5
b)sin B=cosC=√2/54
cosB=sin C=√10/108
tg B=ctgC=2√5/5
ctg B=tgC=√5/2
c)sin²B+2sinC cosC=(√2/54)²+2×√2/54×√10/108=√2/54(√2/54+2√10/108)=
=2/54²(1+√5)=2(1+√5)/2916
d)tg²C-tgB×ctgB=(2/√5)²-1=4/5-1=-1/5
e)(sin C+cosC)²+(sin C-cosC)²=sin²C+2sinCcosC+cos²C+sin ²C-2sinCcosC+cos²C=
=1+1=2
²²²
