Mathematics

Mathematics

Problem

Let xx be any real number. (a) Prove that sin⁡7x−sin⁡3x=2cos⁡5x sin⁡2x\sin 7x-\sin 3x=2\cos 5x\,\sin 2x. (b) Using the result in part (a), transform the equation sin⁡7x=sin⁡3x\sin 7x=\sin 3x into a product form and solve it for 0≤x<2π0\le x<2\pi. a. Prove that sin⁡7x−sin⁡3x=2cos⁡5x sin⁡2x\sin 7x-\sin 3x=2\cos 5x\,\sin 2x. b. Using the result in part (a), transform the equation sin⁡7x=sin⁡3x\sin 7x=\sin 3x into a product form and solve it for 0≤x<2π0\le x<2\pi.

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