Question

已知a为钝角,b为锐角,且sina=4/5,sinb=12/13,则cos(a-b)/2为多少?

Answer 1

cosα=-√1-(sinα)^2=-3/5,cosβ=√1-(sinβ)^2=5/13,

cos(α-β)=cosαcosβ+sinαsinβ=-3/13+48/65=33/65

cos[(α-β)/2]=√[1+cos(α-β)]/2=7√65/65

α-β)/2为锐角,故取正值.