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Misc 2 - Prove (sin 3x + sin x) sin x + (cos 3x - cos x)
Misc 2Prove that: (sin 3𝑥 sin 𝑥) sin 𝑥 (cos 3𝑥 – cos 𝑥) cos 𝑥 = 0Lets calculate (sin 3x sin x) and (cos 3x – cos x) separately We know that sin x sin y = sin ((𝑥 𝑦)/2) cos ((𝑥 − 𝑦)/2)Replacing x with 3x and y with x sin 3x sin x = 2sin ((3𝑥 𝑥)/2) cos ((3𝑥 − 𝑥)/2)
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