Question

sen ( pi + x ) + cos( pi/2 - x ) é, para todo x E R , equivalente a :

Answer 1

Calculando sen(π+x) : sen(π+x) = senπ.cosx+senx.cosπ = 0.cosx-1.senx = -senx . Calculando cos(π/2-x) : cos(π/2-x) = cosπ/2.cosx+senπ/2.senx = 0.cosx+1.senx = senx . Somando , temos : sen(π+x) + cos(π/2-x) = -senx + senx = 0