- sin3x = sin(2x + x)

= sin2x.cosx + cos2x.sinx

= 2sinx.cosx.cosx + (2cos2 – 1).sinx

= 2sinx.cos2x + 2cos2x.sinx – sinx

= 4sinx.cos2x – sinx

= 4sinx.(1 – sin2x) – sinx2

= 3sinx – 4sin3x
 

- Cos3x = cos(2x + x)

= cos2x.cosx – sin2x.sinx

= (2cos2x – 1).cosx – 2sinx.cosx.sinx

= 2cos3x – cosx – 2sin2x.cosx

= 2cosx.(cos2x – sin2x) – cosx

= 2cosx.(cos2x – 1 + cos2x) – cosx

= 2cosx.(2cos2x – 1) – cosx

= 4cos3x – 2cosx – cosx

= 4cos3x – 3cosx