三角涵数解答题

题目

三角涵数解答题
在△ABC中,A、B、C角所对的边分别为a,b,c,且cosA＝2分之根号2,cosB＝2分之根号3
⑴求sin(A＋B)的值
⑵若a-b＝根号2（根号2－1）求c的值

答案

A=π/4
B=π/6
sinA=√2/2,sinB=1/2
(1)
sin(A+B)=sinAcosB+sinBcosA
=(√2/2)*(√3/2)+(√2/2)*(1/2)
=(√6+√2)/4
(2)
a-b=√2(√2-1)
a/b=sinA/sinB=√2
a=b√2
b(√2-1)=√2(√2-1)
b=√2,a=2
A+B=5π/12
C=π-5π/12=7π/12
sinC=sin(A+B)=(√6+√2)/4
a/sinA=c/sinC
c=a*(sinC/sinA)
=2*(√6+√2)*√2/4
=√3+1