5倍根號(hào)3sina+5cosa=8
（根號(hào)3／2）sina＋（1／2）cosa=4/5
sin(π/3)sina+cos(π/3)cosa=4/5
cos(a-π/3)=4/5
因?yàn)閍∈(0,π/3),所以a-π/3∈(-π/3,0)
所以sin(a-π/3)=-根號(hào)(1-(cos(a-π/3))^2)=-根號(hào)(1-(4/5)^)=-3/5
根號(hào)2sinβ+根號(hào)6cosβ=2
2根號(hào)2((1/2)sinb+(根號(hào)3/2)cosb)=2
(1/2)sinb+(根號(hào)3/2)cosb=根號(hào)2/2
sin(π/6)sinb+cos(π/6)cosb=根號(hào)2/2
cos(b-π/6)=根號(hào)2/2
因?yàn)棣隆?π/6,π/2)
所以b-π/6∈(0,π/3)
所以sin(b-π/6)=根號(hào)(1-(cos(b-π/6))^2)=根號(hào)(1-(根號(hào)2/2)^2)=根號(hào)2/2
(1)cos(a+π/6)=cos(a-π/3+π/2)=cos(a-π/3)cos(π/2)-sin(a-π/3)sin(π/2)
=(4/5)*0-(-3/5)*1=3/5
因?yàn)閍∈(0,π/3),所以a+π/6∈(π/6,π/2)
所以sin(a+π/6)=根號(hào)（1-(cos(a+π/6))^2)=根號(hào)(1-(3/5)^2)=4/5
(2)cos(a+b)=cos(a+π/6+b-π/6)=cos(a+π/6)cos(b-π/6)-sin(a+π/6)sin(b-π/6)
=3/5*(根號(hào)2/2)-4/5*(根號(hào)2/2)=- 根號(hào)2/10