4sinasinb=√2
4cosacosb=√6
两式相加
4(cosacosb+sinasinb)=√6+√2
cos(a-b)=(√6+√2)/4
两式相减
4(cosacosb-sinasinb)=√6-√2
cos(a+b)=(√6-√2)/4
cos2a+cos2b
=cos[(a+b)+(a-b)]+cos[(a+b)-(a-b)]
=cos(a+b)cos(a-b)-sin(a+b)sin(a-b)+cos(a+b)cos(a-b)+sin(a+b)sin(a-b)
=2cos(a+b)cos(a-b)
=2*(√6+√2)/4*(√6-√2)/4
=1/2