Simplifying Sin[3θ] to Simplifying Trigonometric Expressions

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The discussion focuses on simplifying Sin[3θ] using trigonometric identities without employing double angles. The initial approach involves applying the sine addition formula, Sin[3θ] = Sin[θ + 2θ], and expanding it to Sin[θ] Cos[2θ] + Cos[θ] Sin[2θ]. The user struggles to simplify the expression to the expected result of 3sinθ - 4sin^3θ, indicating confusion about the necessary formulas. The key formula for Sin[2θ] = 2sinθcosθ is mentioned as a potential aid in the simplification process. Ultimately, the conversation revolves around finding the correct steps to achieve the desired simplification of Sin[3θ].
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Homework Statement


Simplify Sin[3θ] (no double angles)

Homework Equations


Sin[3θ]=Sin[θ+2θ]
Sin[α + β] = Sin[α] Cos[β] + Cos[α] Sin[β]
Sin[3θ] = 3sinθ - 4sin^3 θ
Cos2θ = 1-2Sin^2θ

The Attempt at a Solution


Sin[3θ] = sin[θ+2θ]
Sin[θ+2θ] = Sinθ Cos2θ + Cosθ Sin2θ
Sinθ Cos2θ + Cosθ Sin2θ = Sinθ (1-2Sin^2θ) + Cosθ Sin2θ
=Sinθ - 2Sin^3θ + Cosθ Sin2θ This is where i get lost...I know it should end up being
= (3sinθ - 4sin^3 θ) but i cannot figure out how to get there. I don't know whether I just don't have the formula i need or what.
 
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Sin2θ = 2sinθcosθ, remember that one?
 

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