2sin^2(x)=cos(3п/2-x)

2sin^2(x) = cos(3п/2 - x);
По формулам приведения cos(3п/2 - x) = - sin(x);
2sin^2(x) - cos(3п/2 - x) = 0;
2sin^2(x) + sin(x) = 0;
Вынесем sin(x) за скобки.
sin(x)(2sin(x) + 1) =0;
1) sin(x) = 0; ==gt; x = пk, kZ.
2) 2sin(x) + 1 = 0;
sin(x) = -1/2; ==gt; x = -п/6 + 2пn, nZ; x = -5п/6 + 2пn, nZ;
Ответ: 1) x = пk, kZ; 2) x = -п/6 + 2пn, nZ; x = -5п/6 + 2пn, nZ.