由韦达定理:
sinA +sinB=根号2乘COS40;
sinA乘sinB=COS^2 40 -1/2=COS80 /2.=sin10 /2
(sinA +sinB)^2=sin^2 A +sin^2 B +2 sinA乘sinB = 2乘COS^2 40= COS80 +1=sin10 +1.
则sin^2 A +sin^2 B=sin10 +1 -2 sinA乘sinB =sin10 +1 -2*(sin10 /2)=1.
则sin^2 A=1-sin^2 B=cos^2 B.
则sinA=cosB.
A,B互余.A+B=90.
则B=90-A.
2B-A=180-3A.
所以:COS(2B-A)=cos(180-3A)
=-cos3A.
A,B互余.则sinA乘sinB=sinA乘cosA
=sin10 /2.
则sin(2A) /2=sin10 /2.
2A=10.
则3A=15.
所以:COS(2B-A)=-cos3A=-cos15
=-√[(1+cos30)/2]=-√[(1+√3 /2)/2]
=-√[(√3 /2+1/2)^2 /2]
=-(√3 /2+1/2) /√2
=-√6 /4-√2/4