2tg^2(x) + 4cos^2(x) = 7
ОДЗ: cos(x) =/=(не равно) 0, x =/=(не равно) pi/2 + pi*k
2sin^2(x)/cos^2(x) + 4cos^2(x) - 7 = 0
2sin^2(x) + 4cos^4(x) - 7cos^2(x) = 0
2 - 2cos^2(x) + 4cos^4(x) - 7cos^2(x) = 0
cos^2(x) = t, 0 <= t <= 1 при любом х </span>
4t^2 - 9t + 2 = 0
D = 81 - 4*4*2 = 81 - 32 = 49 = 7^2
t1 = (9 - 7)/8 = 2/8 = 1/4
cos^2(x) = (cos(2x) + 1)/2 = 1/4
cos(2x) = -1/2
2x1 = 2П/3 + 2П*k, x1 = П/3 + П*k
2x2 = 4П/3 + 2П*k, x2 = 2П/3 + П*k