[tex]3sin^{2 }x=2sin2x-1 [/tex]

[Гост]

[tex]3sin^{2 }x=2sin2x-1[/tex]

[KOPMOPAH]

$$3 \sin x^2=2\sin 2x -1 \Leftrightarrow 3 \sin x^2-2\sin 2x +1 =0\Leftrightarrow 3 \sin x^2-4\sin x\cos x +\sin^2 x + \cos^2 x=0$$ $$4\sin^2 x-4\sin x\cos x+\cos ^2x=0|:\cos x\ne 0\Rightarrow 4\tg ^2x-4\tg x+1=0$$ $$\tg x=\frac 12$$