1.

sin 3x = 3 sinx -4 sin’x

Answer»

Sin 3x = sin (2x+x)= sin 2x cos x + cos 2x sin x

= 2sin x cos x cosx + (1–2sin^2x) sin x

= 2 sin x (1–sin^2 x) + (1- 2 sin^2 x) sin x

= 2 sin x - 2 sin ^3 x + sin x - 2 sin^3 x

= 3 sin x - 4 sin^3 x

Hence sin 3x = 3sin x - 4 sin^3 x


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