Question

RESOLVER: senx + cosx=√2, e indicar la menor solucion positiva

Answer 1

senx + cosx=√2

(senx + cosx)²=(√2)²

sen²x + 2senxcosx + cos²x = 2

(sen²x + cos²x) + 2senxcosx = 2

1 + sen2x = 2

sen2x = 1        ⇔     2x = Π/2 + 2Πn   con n∈Z

menor solución positiva n=0  ⇒  2x= Π/2     ∴    x= Π/4

sen( Π/4)  + cos( Π/4) = √2  

(1/√2) + (1/√2) = √2

2/√2 = √2  

 (2×√2)/(√2)² = √2

2×√2/2 = √2

√2 = √2