Решите уравнение: sinx*sin7x = sin3x*sin5x. Created by AlyonaF. algebra-ru

Решите уравнение: sinx*sin7x = sin3x*sin5x...

July 2022 1 13 Report

Решите уравнение: sinx*sin7x = sin3x*sin5x

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Smeshinka13 По формулам sin 7x * sin x = 1/2*[cos(7x - x) - cos(7x + x)] = 1/2*(cos 6x - cos 8x) sin 3x * sin 5x = 1/2*[cos(5x - 3x) - cos(5x + 3x)] = 1/2*(cos 2x - cos 8x) По уравнению cos 6x - cos 8x = cos 2x - cos 8x cos 6x = cos 2x По формуле тройного аргумента cos 3a = 4cos^3 a - 3cos a cos 6x = 4cos^3 2x - 3cos 2x = cos 2x 1) cos 2x = 0 2x = Pi/2 + Pi*k x = Pi/4 + Pi/2*k 2)4cos^2 2x - 3 = 1 cos^2 2x = 1 cos 2x = -1 2x = Pi + 2Pi*k x = Pi/2 + Pi*k 3) cos 2x = 1 2x = 2Pi*k x = Pi*k Ответ: x1 = Pi/4 + Pi/2*k, x2 = Pi/2 + Pi*k, x3 = Pi*k

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