for positive acute angles a and b, it is known that cos(a)=9/41 and sin(b)=28/53. find the value of cos(a+b) in simplest form

Answer 1

cos(a+b) = cosacosb - sinasinb = (9/41)(45/53) - (40/41)(28/53)

=369/41(53) - 1129/41(53) = -760/2173 = -0.35 rounded off

41^2 - 9^2 = 40^2, if cosa=9/41, sina= 40/41 a = about 77.3 degrees

53^2 -45^2 = 28^2 if sinb= 28/53 then cosb = 45/53, b = 31.9 degrees

a+b = 77.3 + 31.9 = 109.2, cos109.2 = -0.33 rounded off