Prove using trig identites

sin(x)=4cos(x/2)⋅cos(x/4)⋅sin(x/4)

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

Trigonometry Trigonometric Functions
Uglybruh4 Uglybruh4
4
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1 Answer

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

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

Savionf Savionf
573
  • Savionf Savionf
    0

    Let me know if you have any further questions.

    • Uglybruh4 Uglybruh4
      +1

      i appreciate it thank you so much

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