Question

sa se demonstreze daca x,y €(0,π/2), sin x=sqrt(5)/5, sin y=sqrt(10)/10 atunci x+y=π/4 (sqrt = radical)

Answer 1

Răspuns:

f.fundam a tyrigonometriei

Explicație pas cu pas:

sinx=√5/5⇒cosx=2/√5

siny=√10/10⇒cosy=3/√10

sin(x+y) =sinxcosy+sinycosx=(√5/5)*3/(√10)+(10/√10)*(2/√5)=

3/5√2+√2/5=3√2/10+2√2/10=5√2/10=√2/2

cum x,y €(0,π/2)si PRESUPUNAND ca x+y∈(0,π/2)⇒ x+y=π/4