To prove: 3sin40° - sin340° = \(\frac{\sqrt{3}}{2}\)
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