Question

Calculati:
sin(arcsin 3/5 + arcsin 4/5)
V-as ruga sa imi explicati si cum ati facut. Multumesc!

Answer 1

Notam arcsin3/5=a si arcsin 4/5=b
sin(a+b)=sin a*cos b+sin b*cos a
Folosind teorema fundamentala a trigonometriei
sin²a+cos²b=1
si sin a=sin(arcsin3/5)=3/5
sin b=sin(arcsin 4/5)=4/5 
cos² a=1-(3/5)²=>cos a=4/5
cos² b=1-(4/5)²=>cos b=3/5
sin(a+b)=sin a*cos b+sin b*cos a=3/5*3/5+4/5*4/5=9/25+16/25=25/25=1