Question

Prove that:  sin3x + sin2x – sin x = 4sinx cos(x/2)cos(3x/2)

Answer 1

We will start with LHS

First Answer:-

Sin 3 x + Sin 2x - Sin x 

= (Sin 3x - Sin x) + Sin 2 x ,;          Sin A- Sin B = 2 Sin (A-B)/2 Cos (A+B)/2

= 2 Sin x Cos 2x + 2 Sin x Cos x   ;  ;  Sin 2 A = 2 Sin A Cos A

= 2 Sin x [ Cos 2x + Cos x ]  ;;     Cos A + Cos B = 2 Cos (A+B)/2 Cos (A-B)/2
 
= 2 Sin x * 2 Cos 3x/2 Cos x/2

= 4 Sin x * Cos x/2 * Cos 3x/2   = RHS

Second answer:-