Tg2x=9sin^2x+4sinxcosx-3cos^x

sin²x = (1-cos2x) / 2; cos²x = (1+cos2x) / 2.

4sinxcosx=2· (2sinxcosx) = 2sin2x.

Уравнение принимает вид:

tg2x-2sin2x=9 (1-сos2x) / 2 - 3 (1+cos2x) / 2

2sin2x (1/cos2x - 2) = 6-12cos2x

2sin2x (1-2cos2x) / cos2x=6 (1-2cos2x)

(1-2cos2x) (tg2x-3) = 0

cos2x≠0

1-2xos2x=0 или tg2x-3=0

cos2x=1/2 tg2x=3

2x = ±arccos (1/2) + 2π·k, k∈Z 2x=arctg3+π·n, n∈Z

2x = ± (π/3) + 2πk, k∈Z x = (arctg3) / 2 + (π/2) ·n, n∈Z

x = ± (π/6) + πk, k∈Z

При х = ± (π/6) + πk и х = (arctg3) / 2 + (π/2) ·n, k, n∈Z

cos2x≠0

О т в е т. х=± (π/6) + πk и х = (arctg3) / 2 + (π/2) ·n, k, n∈Z