cosα=[cos(α/2)]^2-[sin(α/2)]^2
={[cos(α/2)]^2-[sin(α/2)]^2/{[sin(a/2)]^2+[cos(a/2)]^2}
={1-[tan(α/2)]^2}/{1+[(tanα/2]^2}
=(1-1/9)/(1+1/9)=4/5