Given the following information find cosalpha beta sin alph

Given the following information, find cos(alpha + beta) sin alpha = 3/5, 0 lessthanorequalto alpha lessthanorequalto pi/2 and cos beta = 5/13, 0 lessthanorequalto beta lessthanorequalto pi/2 cos(alpha + beta) =

Solution

cos()=5/13 =>sin =((13²-5²))/13 =12/13

sin =3/5=>cos =((5²-3²))/5 =4/5

cos(+)=coscos -sinsin

cos(+)=(4/5)(5/13) -(3/5)(12/13)

cos(+)=(20/65)-(36/65)

cos(+)=-16/65