Question

срочно
2cos^2x +1 =корень из 3 cos (п /2 +x)

Answer 1

$\cos^2{x}=1-\sin^2{x};\\\cos{(\pi/2+x)}=-\sin{x}\\2-2\sin^2{x}+1+\sqrt{3}*\sin{x}=0\\\sin{x}=a\\2a^2-\sqrt{3}a-3=0;D=3+24=3^2*3\\a=\frac{\sqrt{3}б3\sqrt{3}}{4}\\\left[\begin{array}{ccc}\sin{x}=-\sqrt{3}/2\\\sin{x}=\sqrt{3}\\\end{array}!|\sin{x}|\leq1!$

$\sin{x}=-\sqrt{3}/2\\x=(4\pi/3+2pi*n;5\pi/3+2pi*n)$

Ответ: x={ 4π/3+2πn; 5π/3+2πn}, n∈Z.