Prove that: .

Formula: -

(i) sin (A + B) sin (A – B) = sin² A – sin² B

(ii)

(iii) 3sinA – 4sin³A = sin3A

Taking L.H.S we get,

sin A sin (60° – A) sin (60° + A) = sin A (sin² 60° – sin² A) using formula (i)

⇒ sin A sin (60° - A) sin (60° + A) using formula (ii)

⇒ sin A sin (60° - A) sin (60° + A)

⇒ sin A sin (60° - A) sin (60° + A)

⇒ sin A sin (60° - A) sin (60° + A)

using formula (iii)

LH.S = R.H.S

Hence, Proved.