Question

Prove that: 4 sin α sin (α + π ) sin (α + 2 ) = sin 3 α

Answer 1

Step-by-step explanation:

LHS = 4sina sin( a + π/3) sin(a +2π/3)

= 2{ 2sina.sin(a +π/3).sin(a +2π/3)

=2{cos(a -a -π/3) - cos( 2a +π/3) }sin(a +2π/3)

=2×1/2sin(a +2π/3) - 2sin(a +2π/3).cos(2a +π/3)

=sin(a + 2π/3) - sin(3a + π) -sin( a +2π/3)

=sin3a =RHS