Question

Taking x = π/6 verify: sin3x = 3sinx - 4sin³ x.

Answer 1

\(x = \frac \pi 6\)

L.H.S = \(sin3x = sin(3\times \frac\pi6) = sin\frac\pi2 = 1\)

R.H.S. = \(3sinx - 4sin^3x = 3sin(\frac \pi6) - 4sin^3(\frac\pi 6)\)

\(= \frac 32 - 4(\frac12)^3 = \frac 32 - \frac 48 = \frac 32-\frac 12 = \frac 22 = 1\)

L.H.S. = R.H.S.

Hence verified that at \(x =\frac \pi6, sin3x = 3sin x - 4sin^3 x\).