Question

24cosx - 8cos2x=15

Срочно нужно решить! Помогите пожалуйста.

Answer 1

$24cosx - 8cos2x=15\\cos2x = 2cos^{2}x - 1 \\24cosx -8(2cos^{2}x - 1) = 15\\16cos^2x-24cosx +7 = 0\\cosx = t\\16t^2 - 24t + 7 = 0\\t_{1} = \frac{3}{4} + \frac{1}{2\sqrt{2} } \\ t_{2} = \frac{3}{4} - \frac{1}{2\sqrt{2} }\\x = \pm arccos(\frac{3}{4} - \frac{1}{2\sqrt{2} })+2\pi k,k \in Z$