Question

Prove that: (sin3x+sinx)sinx+(cos3x-cosx)cosx=0

Answer 1

here is the answer again sorry for my writing skill

Answer 2

Answer:

(sin3x+sinx)sinx+(cos3x-cosx)cosx = 0

Step-by-step explanation:

(sin3x+sinx)sinx+(cos3x-cosx)cosx

Using SinA  + SinB  = 2Sin((A + B)/2) Cos((A-B)/2)

& CosA - CosB  = - 2Sin((A + B)/2) Sin((A-B)/2)

Here A = 3x  B = x

= (2 Sin2x * Cosx )Sinx  + (- 2Sin2x * Sinx) Cosx

= 2Sin2x CosxSinx  -  2Sin2xSinxCosx

= 0

= RHS

QED

Proved

(sin3x+sinx)sinx+(cos3x-cosx)cosx = 0