To prove:

Taking LHS,

= 3 sin 40° - sin³ 40° …(i)

We know that,

sin 3x = 3 sinx – sin³x

Here, x = 40°

So, eq. (i) becomes

= sin 3(40°)

= sin 120°

= sin (180° - 60°)

= sin 60° [∵sin (180° - θ) = sin θ]

= RHS

∴ LHS = RHS

Hence Proved