Question

24cosx - 8cos2x=15

Срочно нужно решить! Помогите пожалуйста.

Answer 1

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