Question

Aratati ca sin(a+b)= 63/65, stiind ca a,b apartin intervalului (0, pi/2), sin a=3/5 si sin b=12/13

Answer 1

a si b sunt in primul cadran iar sin²x+cos²x = 1 ⇒ cos a = 4/5, cos b =5/13.
Inlocuim in relatia:
sin (a+b) = (sin a)(cos b) + (sin b)(cos a) = (3/5)*(5/13) + (12/13)*(4/5) = 15/65 + 48/65 = 63/65