Răspuns:
intr-un triunghi dreptunghic (fie A=90) avem
sinB=cateta opusa lui/ipotenuza=cosC
cosB=cateta alaturata lui/ipotenuza=sinB
tgB=sinB/cosBcateta opusa lui/cateta alaturata lui=ctgC
ctgB=1/tgB=cateta alaturata lui/cateta opusa=tgC
Explicație pas cu pas:
cu Pitagora aflam lungimea ipotenuzei:
BC=√(AB²+AC²)=24√3 cm
a) si b)
sinB=AC/BC=6√30/24√3=√10/4=cosC
cosB=18/√2/24√3=√6/4=sinC
tgB=sinB/cosB=√10/4 * 4/√6=√5/√3=√15/3=ctgC
ctgB=3/√15=√3/√5=√15/5=tgC
c)
sin²B+2sinCcosC=10/16+2√6/4 * √10/4=(10+4√15)/16=(5+2√15)/8
d) calcul...
e)
(sinC+cos)²+(sinC-cosC)²=sin²C+2sinCcosC+cos²C+sin²C-2sinCcosC+cos²C=2*(sin²C+cos²C)=2*1=2
