Question

МАТ ПРОФ 13 ЗАДАНИЕ​

Answer 1

a)

$sqrt{3}cos(x)+2cos(x-frac{5pi}{6})=cos(2x)\sqrt{3}cos(x)+2(cos(x)cos(frac{5pi}{6})+sin(x)sin(frac{5pi}{6}))=cos(2x)\sqrt{3}cos(x)+2(-frac{sqrt{3}}{2}cos(x)+frac{1}{2}sin(x))=cos(2x)\sqrt{3}cos(x)-sqrt{3}cos(x)+sin(x)=cos(2x)\sin(x)=cos(2x)\sin(x)=1-2sin^2(x)\2sin^2(x)+sin(x)-1=0\D=1+8=9\sin(x)=frac{1}{2};-1\x=frac{pi}{6}+2pi k\x=frac{5pi}{6}+2pi k\x=frac{3pi}{2}+2pi k$

б)

$-frac{9pi}{2};-frac{31}{6}$