Sin [latex] \frac{4x}{3} [/latex]=[latex] cos^{2} [/latex][latex] \frac{x}{3} [/latex]-[latex] sin^{2} [/latex][latex] \frac{x}{3} [/latex]sin 4x/3 = cos^2 x/3 - sin^2 x/3

Question

Sin [latex] \frac{4x}{3} [/latex]=[latex] cos^{2} [/latex][latex] \frac{x}{3} [/latex]-[latex] sin^{2} [/latex][latex] \frac{x}{3} [/latex]sin 4x/3 = cos^2 x/3 - sin^2 x/3

Sin [latex] \frac{4x}{3} [/latex]=[latex] cos^{2} [/latex][latex] \frac{x}{3} [/latex]-[latex] sin^{2} [/latex][latex] \frac{x}{3} [/latex] sin 4x/3 = cos^2 x/3 - sin^2 x/3

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Ответ(ы) на вопрос:

Accepted Answer

[latex]sin\frac{4x}3=cos^2\frac{x}3-sin^2\frac{x}3\\ 2sin\frac{2x}3cos\frac{2x}3=\frac{1+cos\frac{2x}3}{2}-\frac{1-cos\frac{2x}3}{2}\\ 2sin\frac{2x}3cos\frac{2x}3=2cos\frac{2x}3\\ sin\frac{2x}3=1\\ \frac{2x}3=\frac{\pi}2\pm\pi n\\ x=\frac{3\pi}4\pm\frac{3}2\pi n[/latex]