Question

Aratati ca ( 2sin x + cos x )² + (sin x + 2cos x ) - 4sin 2x = 5 pentru x ∈ R .

Answer 1

[tex](2sinx+cosx)^2+(sinx+2cosx)^2-4sin2x=5\\ 4sin^2x+4\cdot sinx\cdot cos x+cos^2x+sin^2x+4\cdot sinx\cdot cosx+\\ +4cos^x-4sin2x=5\\ 5sin^2x+5cos^2x+8\cdot sinx\cdot cosx-4sin2x=5\\ 5(sin^2x+cos^2x)+4\cdot2\cdot sinx\cdot cosx-4\sin 2x=5\\ 5+4sin2x-4sin2x=5\\ \boxed{5=5(A)}[/tex]