Question

(a) Prove that sin 3x + sin 2x – sin x = 4 sin x cos(x/2) cos (3x/2)​

Answer 1

Answer:

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Step-by-step explanation:

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