(1-2sin^2(pi+a))/(sin(pi/2+a)+sin(pi-a)) + (1-2cos^2(pi-a))/(cos(pi+a)+cos(pi/2+a))

Question

Алгебра: (1-2sin^2(pi+a))/(sin(pi/2+a)+sin(pi-a)) + (1-2cos^2(pi-a))/(cos(pi+a)+cos(pi/2+a))

МИЛ567 · Accepted Answer

1) cos2x - 9cosx + 8 = 0
2cos²x - 1 - 9cosx + 8 = 0
2cos²x - 9cosx + 7 = 0
D = 81 - 4*2*7 = 25
cosx = t, I t I  ≤ 1
2t² - 9t + 7 = 0
t₁ = (9 - 5)/4
t₁ = 1
t₂ = (9 + 5)/4
t₂ = 7/2 не удовлетворяет условию  I t I  ≤ 1
cosx = 1
x = 2πk, k∈Z

2) 3cosx + sinx = 0 делим на cosx ≠ 0
3 + tgx = 0
tgx = - 3
x = - arctg(3) + πn, n∈Z

3) 3sin2x + sinxcosx - 2cos2x = 0
3sin2x + 1/2sin2x - 2cos2x = 0
3,5* sin2x - 2cos2x = 0   делим на cos2x ≠ 0
3,5tg2x - 2 = 0
tg2x = 4/7
2x = arctg(4/7) + πn, n∈Z
x = (1/2)*arctg(4/7) + πn/2, n∈Z

MOGZ ответил