Đáp án:
`A=2`
`B=-2+\sqrt3`
Giải thích các bước giải:
`A=(cosa+cosb)^2+(sina+sinb)^2`
`=cos^2a+2cosacosb+cos^2b+sin^2a+2sina sinb+sin^2b`
`=(cos^2a+sin^2a)+(cos^2b+sin^2b)+2(cosacosb+sinasinb)`
`=1+1+2cos(a-b)`
`=2cos(a-b)+2`
`=2cos (π/3) +2`
`=2`
.
`B=(cosa+sinb)^2+(sina-cosb)^2`
`=cos^2a+2cosasinb+sin^2b+sin^2a-2sinacosb+cos^1b`
`=(cos^2a+sin^2a)+(sin^2b+cos^2b)-2(sinacosb-cosasinb)`
`=1+1-2sin(a-b)`
`=2sin(a-b)+2`
`=-2. sin (π/3) +2`
`=-2+\sqrt3`
