Question

sin A .sin(60-A).sin(60+A)​

Answer 1

Solution:-

L.H.S. = sin A sin (60° - A) sin (60° + A)

= sin A [ sin² 60° - sin² A]      {sin (A + B) sin (A - B) = sin² A - sin² B }

= sin A [3/4 - sin² A]

= (3sin A)/4 - sin³ A = 1/4 [3sin A - 4sin³ A]

= 1/4sin³ A = R.H.S.

Hence proved.