Question

Решите sin2x-√3*sinx-√2*cosx+√6/2=0

Answer 1

2sin x*cos x - sgrt3*sin x - sgrt2*cos x + sgrt3*sgrt2/ 2 = 0;
(2 sin x*cos x - sgrt2*cos x) - (sgrt3*sin x - sgrt3/sgrt2)= 0;
(sgrt2*sgrt2*cos x - sgrt2*cosx) - (sgrt3*sinx - sgrt3/sgrt2)=0;
sgrt2*cosx(sgrt2*sinx - 1) - sgrt3(sin x - 1/sgrt2)=0;
sgrt2*cosx(sgrt2*sinx - 1) - sgrt3/sgrt2(sgrt2*sin x - 1)=0;
(sgrt2*sin x - 1)(sgrt2*cos x - sgrt3/sgrt2)=0;
1) sgrt2*sinx - 1 = 0;
 sin x = 1/sgrt2;
sin x = sgrt2/2;
x = (-1)^k * pi/4 + pi*k; k-Z
2) sgrt2*cos x - sgrt3/ sgrt2= 0;
cosx = sgrt3/2;
x = + - pi/3 + 2 pi*k; k-Z

Answer 2

ошибка в конце cos x = sgrt3/2; x = + - pi/6 + 2pi*k; k-Z