`a)4sin^2 -cos^2 x+sin x cos x=2`
`@TH1:cos x =0<=>x=\pi/2+k\pi` `(k in ZZ)`
Ptr có dạng: `4sin^2 x=2<=>sin^2 x=1/2` (Vô lí)
`@TH2:cos x \ne 0<=>x \ne \pi/2+k\pi`
`=>4tan^2 x-1+tan x=2+2tan^2 x`
`<=>2tan^2 x+tan x-3=0`
`<=>[(tan x=1),(tan x=-3/2):}<=>[(x=\pi/4+k\pi),(x=arc tan(-3/2)^2+k\pi):}` `(k in ZZ)` (t/m)
_____________________________________
`b)2sin^2 x-\sqrt{3}sin 2x=2`
`<=>2[1-cos 2x]/2-\sqrt{3}sin 2x=2`
`<=>1-cos 2x-\sqrt{3}sin 2x=2`
`<=>\sqrt{3}sin 2x+cos 2x=-1`
`<=>\sqrt{3}/2sin 2x+1/2cos 2x=-1/2`
`<=>sin (2x+\pi/6)=-1/2`
`<=>[(2x+\pi/6=-\pi/6+k2\pi),(2x+\pi/6=[7\pi]/6+k2\pi):}`
`<=>[(x=-\pi/3+k\pi),(x=\pi/2+k\pi):}`
_____________________________________
`c)2sin 2x+2sin^2 x=3`
`<=>4sin x cos x+2sin^2 x=3`
`@TH1:cos x=0<=>x=\pi/2+k\pi` `(k in ZZ)`
Ptr có dạng: `2sin^2 x=3<=>sin^2 x=3/2` (Vô lí)
`@TH2:cos x \ne 0<=>x \ne \pi/2+k\pi` `(k in ZZ)`
`=>4tan x+2tan^2 x=3+3tan^2 x`
`<=>tan^2 x-4tan x+3=0`
`<=>[(tan x=1),(tan x=3):}<=>[(x=\pi/4+k\pi),(x=arc tan(3)+k\pi):}` `(k in ZZ)` (t/m)
