Question

решить
cos^2 x +4sinxcosx = 5sin^2 x ​

Answer 1

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Answer 2

$\cos(x ) {}^{2} + 4 \sin(x) \cos(x) = 5 \sin(x) {}^{2} \\ 5 \sin(x) {}^{2} - 4 \sin(x) \cos(x) - \cos(x) {}^{2} = 0$

Делим на

${ \cos(x) }^{2}$

получим

$5 \tan(x) {}^{2} - 4 \tan(x) - 1 = 0 \\ \tan(x) {}^{2} = {y} \\ 5y {}^{2} - 4y - 1 = 0 \\ y1 = 1 \\ y2 = - \frac{1}{5} \\ \tan(x) = 1 \\ \tan(x) = - \frac{1}{5} \\ x = \frac{\pi}{4} + \pi \times k \\ x = - arctan( \frac{1}{5} ) + \pi \times k \\$

k € Z