Question

а)4sin²x + 4sinx - 3 = 0
б)sin²x + sinx cosx - 2 cos²x = 0
в)cos2x - cosx = cos3x

Answer 1

б)sin^2x + sinxcosx - 2cos^2x = 0  | : cos^2x

tg^2x + tgx - 2 = 0

делаем замену tgx = t;

t^2 + t - 2 = 0;
d= 1 - 4 * 1 * (-2) = 9

t1= -1+3 /2 = 1     ;    t2 = -1-3/2 = -2 ;

tgx = 1                    ;         tgx = -2
x = p/4 + pk, k e z    ;     x = arctg(-2) + pn, n e z

ответ: p/4 + pk, k e z  ;   x = arctg(-2) +pn, n e z.