6sin^2x=5sin(3pi/2-x)+2

Question

6sin^2x=5sin(3pi/2-x)+2

Answer 1

6 sin^2 x = 5 sin (3pi/2  - x) + 2;
6 sin^2 x = - 5 cos x + 2;
6 sin^2 x + 5 cos x - 2 = 0;
6(1- cos^2 x ) + 5 cos x - 2 = 0;
6 - 6 cos^2 x + 5 cos x - 2= 0;
6 cos^2 x - 5 cos x - 4 = 0;
D = 25+144= 121= 11^2;
cos x = (5+11)/12= 16/12= 4/3 > 1; нет решений.
сos x = - 1/2;    x = + - pi/3 + 2pi*k; k-Z