Решите уравнение:

4sin2x+3cos2x=5

4sin2x + 3cos2x=5

4*2sinxcosx + 3 (cos²x - sin²x) = 5 (cos²x + sin²x)

8sinxcosx + 3cos²x - 3sin²x - 5cos² - 5sin²x = 0

- 8sin²x + 8sinxcosx - 2cos²x = 0

(- 8sin²x + 8sinxcosx - 2cos²x) / - cos²x = 0

8tg²x - 8tgx + 2=0 x≠ π/2 + πn n∈ Z

tgx = y

8 у² - 8 у + 2=0

d=64 - 4*2*8 = 64 - 64 = 0

у = - 8 / 16 = - 1/2

tgx=-1/2

x = arctg (-1/2) + πn n∈Z