Prove using trig identites


theres a part where you use sinx=2sin(x/2) * cos(x/2) but im a little lost

1 Answer

You just need to use the identity $\sin \theta = 2 \cos(\frac{\theta}{2})\sin (\frac{\theta}{2})$ twice. We have 

\[\sin x = 2 \cos(\frac{x}{2})\sin (\frac{x}{2})=2 \cos(\frac{x}{2})[2 \cos(\frac{x}{4})\sin (\frac{x}{4}) ]\]
\[=4 \cos(\frac{x}{2}) \cos(\frac{x}{4})\sin (\frac{x}{4}).\]

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