Cosa=5/6⇒sina=-√(1-cos²a)=-√(1-25/36)=-√(11/36)=-√11/6
sinb=-2/3⇒cosb=√(1-sin²b)=√(1-4/9)=√(5/9)=√5/3
sin(a+b)=sinacosb+cosasinb=-√11/6*√5/3-2/3*5/6=-√55/18-10/18=
=-(√55+10)/18
sin(a-b)=sinacosb-cosasinb=-√11/6*√5/3+2/3*5/6=-√55/18+10/18=
=(10-√55)/18
cos(a-b)=cosacosb+sinasinb=5/6*√5/3+√11/6*2/3=5√5/18+2√11/18
=(5√5+2√11)/18
ctg(a-b)=cos(a-b)/sin(a-b)=(5√5+2√11)/18:(10-√55)/18=(5√5+2√11)/(10-√55)=
(5√5+2√11)(10+√55)/(100-55)=(50√5+25√11+20√11+22√5)/45=
=(72√5+45√11)/45=(8√5+5√11)/5