已知sina=2/3,a属于(π/2,π),cosb=-3/4,b属于(π,3π/2),求cos(a+b)和cos(a-b)
问题描述：
已知sina=2/3,a属于(π/2,π),cosb=-3/4,b属于(π,3π/2),求cos(a+b)和cos(a-b)
答
cosa=√5/3 sinb=√7/4
cos(a+b)=2/3*√7/4--3/4*√5/3=(2√7+3√5)/12
cos(a-b)=2/3*√7/4+-3/4*√5/3=(2√7-3√5)/12
答
cosa=-√5/3 sinb=-√7/4
cos(a+b)=cosacosb-sinasinb=(3√5+2√7)/12
cos(a-b)=cosacosb+sinasinb=(3√5-2√7)/12
答
∵sina=2/3,a属于(π/2,π)
∴cosa=-√5/3
∵cosb=-3/4,b属于(π,3π/2)
∴sinb=-√7/4
∴cos(a+b)=cosacosb-sinasinb
=(-√5/3)*(-3/4)-(2/3)*(-√7/4)
=(3√5+2√7)/12
cos(a-b)=cosacosb+sinasinb
=(-√5/3)*(-3/4)+(2/3)*(-√7/4)
=(3√5-2√7)/12