Question

Помогите решить √2*sin(2x)*sin(х+п/4)=2sin(п/4)

Answer 1

(cos pi/4*cos 2x + sin pi/4*sin 2x) - √2sinx = √2(sin2x + 1)

2(√2/2*cos 2x + √2/2 *sin2x) - √2sinx = √2(sin 2x +1);

2*√2/2 (cos 2x + sin 2x) - √2sinx = √2(sin 2x +1);

cos2x + sin 2x -sinx = sin 2x +1;

1 - 2sin^2 x - sinx = 1;

-sinx(2sinx+1)=0;

1) sinx = 0; x1=pin, n---Z.

2) 2sinx+1=0; sinx= -1/2; x2=(-1)^n(-pi/6)+pin, n---Z.