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Use a product-to-sum formula to rewrite sin 4w sin 2w as a sum or difference. sin 4w sin 2w=

Use a product-to-sum formula to rewrite sin⁡4wsin⁡2w \sin 4 w \sin 2 w as a sum or difference.\newlinesin⁡4wsin⁡2w= \sin 4 w \sin 2 w=

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Q. Use a product-to-sum formula to rewrite sin⁡4wsin⁡2w \sin 4 w \sin 2 w as a sum or difference.\newlinesin⁡4wsin⁡2w= \sin 4 w \sin 2 w=
  1. Use Product-to-Sum Formula: We will use the product-to-sum formula: sin⁡Asin⁡B=12[cos⁡(A−B)−cos⁡(A+B)]\sin A \sin B = \frac{1}{2} [\cos(A - B) - \cos(A + B)]. Let's substitute A=4wA = 4w and B=2wB = 2w into the formula.
  2. Apply Formula with Specific Values: Apply the product-to-sum formula with A=4wA = 4w and B=2wB = 2w.sin⁡4wsin⁡2w=12[cos⁡(4w−2w)−cos⁡(4w+2w)]\sin 4w \sin 2w = \frac{1}{2} [\cos(4w - 2w) - \cos(4w + 2w)]
  3. Simplify Cosine Arguments: Simplify the arguments of the cosine functions. sin⁡4wsin⁡2w=12[cos⁡(2w)−cos⁡(6w)]\sin 4w \sin 2w = \frac{1}{2} [\cos(2w) - \cos(6w)]
  4. Final Simplified Expression: This is the final simplified expression using the product-to-sum formula. \newlinesin⁡4wsin⁡2w=12cos⁡(2w)−12cos⁡(6w)\sin 4w \sin 2w = \frac{1}{2} \cos(2w) - \frac{1}{2} \cos(6w)

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