Question

cos(a-b)=-2分之1,sin(a+b)=2分之根3,a -b∈(π,2分之3π),a+b∈(0,2分之π),则c

Answer 1

∵cos(a-b)=-1/2且a -b∈(π,3/2π)

∴a-b=4/3π; ……①

又∵sin(a+b)=2分之根3且a+b∈(0,π/2)

∴a+b=π/3; ……②

联立①②可得到2a=5/3π,

∴cos2a=1/2.