PreCalculus - Trigonometry: Trig Identities (32 of 57) Proof Half Angle Formula: sin(x/2)

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In this video I will introduce the half-angle formula sin(x/2)=?
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Is it possible to use one of the other base identities to prove this like Sin2x or something? Trying to get get an idea of the intuition behind going straight to using the Sin^2x vs another. I love the simplicity in this one but wondering if there are other ways

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