jd141751 jd141751

11-04-2017
Mathematics

contestada

Prove the following identity.
sin 3θ = 3 sin θ − 4 sin3 θ

Respuesta :

11-04-2017

I'll work in x because I'm on my phone.

Proof: LHS = sin3x = sin(2x + x)
= sin2x cosx + cos2x sinx
= 2sinxcos^2x + cos^2x sinx - sin^3x
= 2sinx (1 - sin^2x) + sinx (1 - sin^2x) - sin^3x
= 2sinx - 2sin^3x + sinx - sin^3x - sin^3x
= 3sinx - 4sin^3x = RHS

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