Question

Por favor resolvam
(a. Sena- b.cosx)^2 + (a.cosx+ b.cosx)^2 =a^2 + b^2

Answer 1

Resposta:

Explicação passo-a-passo:

(a.senx-bcosx)²= a².senx²- 2a.b.senx.cosx - b².cosx²

(a.cosx+b.senx)²=a².cosx²+2.a.b.senx.cosx + b².senx²

substituindo na equacao dada

a².senx²- 2a.b.senx.cosx - b².cosx²+a².cosx²+2.a.b.senx.cosx + b².senx²

=a².senx² + b².cosx²+a².cosx²+ b².senx²

=a².senx² +a².cosx²+ b².senx² + b².cosx²

=a²(senx²+cosx²)+ b²(senx²+cosx²)

mas

senx²+cosx²=1

=a²+b²

c.q.d.