Question

Aratati ca $sin(3 \pi /2+x)-sin(3 \pi /2-x)=0$ pentru orice x∈ R .

Answer 1

sin(3π/2*cosx+cos3π/2sinx-(sin3π/2cosx-cos3π/2*sinx)=
-cosx+0-(-1*cosx-0)=-cosx+cosx=0

Answer 2

sin(3π/2 +x) -sin(3π/2 -x)=0
sin3π/2*cosx+sinx*cos3π/2-sin3π/2*cosx+sinx*cos3π/2=0
-cosx+0+cosx+0=0
 -cosx si cosx se reduc
=> 0=0 (Adevarat)
3π/2= 3*180/2= 270